Cap03

Name:

Chapter 3 Pretest Form A

Date:

Graph. 1. y = 3x – 4

1. y

x

2. y = − x 2

2. y

x

3. y = 2 x

3. y

x

4. x = –2

4. y

x

5. f(x) = 4

5. y

x

74

Chapter 3 Pretest Form A (cont.) 6. Graph using x- and y-intercepts. 2x – 5y = 10

Name:

6. y

x

For problems 7–9, use the relation {(–7, 9), (4, –7), (8, 2), (2, 9)}. 7. Find the domain of the relation.

7. ____________________________

8. Find the range of the relation.

8. ____________________________

9. Is the relation a function?

9. ____________________________

Determine whether the following relations are functions. 10.

10. ____________________________ y 4 2 –4 –2 –2

2

4

x

–4

11.

11. ____________________________ y 4 2 –4 –2 –2

2

4

x

–4

12. If f ( x) = 3x 2 + 5, find f(–1).

12. ____________________________

13. Determine the slope and y-intercept of the equation 2x + 3y = 12.

13. ____________________________

14. Determine the slope of the line y = 7.

14. ____________________________

15. Determine the slope of the line through the points (–2, 6) and (3, –4). 15. ____________________________ 16. Determine whether or not the graphs of the two equations are parallel. 2 x + y = −5 4x + 2 y = 1

75

16. ____________________________

Chapter 3 Pretest Form A (cont.) 17. Find the equation of the line through (2, –1) with slope 3.

Name:

17. ____________________________

For problems 18–19, let f ( x) = 3 x 2 − 5 and g(x) = x + 9. 18. Find (f + g)(x).

18. ____________________________

19. Find (f + g)(–3).

19. ____________________________

20. Graph y < 5 – x.

20. y

x

76

Name:

Chapter 3 Pretest Form B

Date:

Graph. 1. y = 4 – 2x

1. y

x

2. y = x 2 − 5

2. y

x

3. y = − x

3. y

x

4. x = 5

4. y

x

5. f(x) = –1

5. y

x

77

Chapter 3 Pretest Form B (cont.) 6. Graph using x- and y-intercepts. 3x – 5y = 15

Name:

6. y

x

For problems 7–9, use the relation {(7, 2), (–4, 3), (5, 2), (–3, –1)}. 7. Find the domain of the relation.

7. ____________________________

8. Find the range of the relation.

8. ____________________________

9. Is the relation a function?

9. ____________________________

Determine whether the following relations are functions. 10. ____________________________

10. y 4 2 –4

–2

4

x

–4

11. ____________________________

11. y 4 2 –4

–2

4

x

–4

12. If f ( x) = x 2 + 7 x + 9, find f(–1).

12. ____________________________

13. The yearly profit, p, for Grandma’s Bakery on frozen pies can be estimated by the function p(x) = 2.8x – 12,000, where x is the number of pies sold. Use the function to estimate the profit on 15,000 pies.

13. ____________________________

14. Determine the slope and y-intercept of the graph 7x – 6y = 12.

14. ____________________________

15. Determine the slope of the line through the points (–2, 6) and (3, –5).

15. ____________________________

78

Chapter 3 Pretest Form B (cont.)

Name:

16. Determine whether or not the graphs of the two equations are parallel. 4x − 9 y = 1 8 x = 18 y + 4

16. ____________________________

17. Find the equation of the line through (–2, 4) with slope –3.

17. ____________________________

For problems 18–19, let f ( x) = 4 x 2 − 10 and g(x) = x + 2. 18. Find (f + g)(x).

18. ____________________________

19. Find (f + g)(–2).

19. ____________________________

20. Graph y > x – 4

20. y

x

79

Mini-Lecture 3.1 Graphs Learning Objectives: 1. 2. 3. 4. 5. 6.

Plot points in the Cartesian coordinate system. Draw graphs by plotting points. Graph nonlinear equations. Use a graphing calculator. Interpret graphs. Key vocabulary: Cartesian coordinate system, quadrant, x-axis, y-axis, origin, ordered pair, coordinates, graph, collinear, linear, linear equation, first-degree equations

Examples: 1. Plot the following points on the same set of axes. a) A(4, 2) b) B(3, –5) d) D(–3, –1)

e) E(1, 0)

c) C(–2, 4) f) F(0, –4)

2. Determine whether the following ordered pairs are solutions to the equation y = 3 x − 2. a) (4, 10) b) (–2, –4)

3. Graph each equation. a) y = 2 x + 1

b) y = 1 − x 2

c) y = x − 1

4. Determine the quadrant in which each point is located. a) (–4, 7) b) (5, –1)

c) (–20, –50)

5. Refer to Example 8 from Section 3.1 and decide which of the given graphs best illustrates the following situation. A plane sat on the runway for 20 minutes and then took off, increasing its speed to 600 mph over the next 20 minutes. The plane flew at about 600 mph for about 2 hours. For the next 20 minutes, the plane steadily slowed down until the speed reached about 400 mph. The plane then flew at 400 mph for 20 minutes. The speed of the plane was then quickly reduced in preparation to land. After landing, the plane was forced to hurry off the runway and, as a result, the speed of the plane increased to about 100 mph. Finally, the plane began slowing down as it approached the gate. Teaching Notes: • Students often place ordered pairs having 0 as one its coordinates on the wrong axis. • Emphasis the importance of using parentheses when expressing the coordinates of an ordered pair. Indicate that (3, 5), {3, 5}, and 3, 5 all have different mathematical meanings.

Answers: 1) see Chapter 3 Answers; 2a) yes; 2b) no; 3) see Chapter 3 Answers; 4a) II; 4b) IV; 4c) III; 5) (b)

80

Mini-Lecture 3.2 Functions Learning Objectives:

1. 2. 3. 4. 5. 6.

Understand relations. Recognize functions. Use the vertical line test. Understand function notation. Applications of functions in daily life. Key vocabulary: dependent variable, independent variable, relation, function, domain, range, vertical line test, function notation

Examples:

1. Determine if the following relation is a function. $35 $45 $25 $40

jeans shirt

2. Determine if the following relations are functions. Give the domain and range of each relation or function. a) {(7, –4), (5, 1), (4, 8)} b) {(3,8), (–2,8), (0,8)} c) {(–6, 7), (–6, 2), (–6, 10)} 3. Use the vertical line test to determine whether the following graphs represent functions. Also give the domain and range of each function or relation. y y b) a)

−4 −2

4

4

2

2

−2

2

4

x

−4 −2

2

4

x

−4

−4

4. If f ( x) = −2 x 2 + 3x − 1, find a) f (3) b)

−2

f (−1)

c)

f (0)

5. Suppose that the total profit, in dollars, at local theater can be determined by the function P ( x) = − x 2 + 35 x − 150, where x is the cost, in dollars, of an individual ticket. Determine the value of P (10) and interpret its meaning. Teaching Notes:

• A short phrase to help remember whether a relation involving x-values and y-values is a function is “For each different x-value, there can only be one y-value.” • Elements of the domain can be thought of as input values; elements of the range can be thought of as output values. • Emphasize to students that function notation is not to be confused with multiplication. The notation f ( x) does not mean to multiply f and x. Answers: 1) not a function; 2a) yes, D:{4, 5, 8}, R:{–4, 1, 8}; 2b) yes, D:{ –2, 0, 3}, R:{8}; 2c) no, D:{–6}, R:{2, 7, 10}; 3a) yes, D: \, R: \ ; 3b) no, D: { x x ≥ -4} , R: \ ; 4a) –10; 4b) –6; 4c) –1; 5) P(10)= 100, When tickets are sold at $10 each, the total profit will be $100. 81

Mini-Lecture 3.3 Linear Functions: Graphs and Applications Learning Objectives:

1. 2. 3. 4. 5. 6.

Graph linear functions. Graph linear functions using intercepts. Graph equations of the form x = a and y = b. Study applications of functions. Solve linear equations in one variable graphically. Key vocabulary: linear function, x-intercept, y-intercept, constant function

Examples:

1. Graph each equation.

1 f ( x) = − x 3 2. Graph each equation using the x- and y-intercepts. 1 a) 2 x − 3 y = 6 b) f ( x) = − x + 3 2 3. Graph each line. b) y = −4 a) x = 3 a) y = 2 x − 3

b)

4. Wayne is told that his total monthly salary in his new sales job will be $900 plus 8% commission on his monthly sales. a) Write a function expressing Wayne’s monthly salary, s, in terms of his monthly sales, x. b) Draw a graph of Wayne’s monthly salary versus his monthly sales, for up to and including $10,000 in sales. c) What is Wayne’s monthly salary if his sales are $8000? d) If Wayne’s monthly salary was $1420, what were his monthly sales? 5. Solve equation 3 x + 5 = 2 x + 9 graphically as shown in Example 9 in Section 3.3 Teaching Notes:

• Remind students that f ( x) and y are interchangeable. • Students often graph the line x = 3 as a single point (3, 0). Indicate that in one dimension, x = 3 is a point, but in two dimensions, x = 3 is a line. You may even ask your students to guess what the graph of x = 3 is in three dimensions. y

Answers: 1)

y

2)

y = 2x − 3

4

−4 −2

−2

2

4

x f (x ) = − _1 x

2 4 −2 (0,−2) −4

−4 −2

3

−4

4b)

s Monthly Salary (dollars)

4a) s = 0.08x + 900 ;

x=3

4

4 (0, 3) 2 (3, 0)

2

y

3) 2x − 3y = 6 (6, 0) x 1 f(x ) = − _ x + 3 2

2 −4 −2

−2

2

4c) $1540; 4d) $6500; 5) x = 4

2000 (10000, 1700) 1000 (0, 900) 5000 10000 Monthly Sales (dollars)

x

82

4

x y = −4

Mini-Lecture 3.4 The Slope-Intercept Form of a Linear Equation Learning Objectives: 1. Understand translations of graphs. 2. Find the slope of a line. 3. Recognize slope as a rate of change. 4. Write linear equations in slope-intercept form. 5. Graph linear equations using the slope and the y-intercept. 6. Use the slope-intercept form to construct models from graphs. 7. Key vocabulary: translation, parallel, slope, positive slope, zero slope, negative slope, vertical line (undefined slope), rate of change, slope-intercept form Examples: 1. Find the slope of the line through the given points. a) (3, 7) and (9, 12) b) (0, 3) and (4, 1) c) (2, –4) and (3, 7) d) (–5, 7) and (–2, –1) e) (4, 3) and (8, 3) f) (10, 4) and (10, –1) 2. Find the slope of the line in each figure. Then write and equation of the given line. y y b) a) 4

4

2

2

−4 −2 −2 −4

2

4

x

−4 −2

−2

2

4

x

−4

3. Refer to Example 2 from Section 3.4. a) Determine the slope of the line segment between 1990 and 2002. Round off to two decimal places. b) Explain what the answer to part (a) means in terms of the U.S. public debt. 4. Write each equation in slope-intercept form (if not given in that form). Determine the slope and y-intercept and then use them to draw the graph of the linear equation. b) −3 x + 5 y = −15 c) 3x + 2 y = 6 a) y = −3x + 5 5. Suppose the number of U.S. residents over the age of 65 is approximated by the equation y = 0.5 x + 31, where x is the number of years since 1990, and y is measured in millions of people. Use this equation to predict the number of U.S. residents in 2015 over the age of 65. Teaching Notes:

• Another common word definition for slope related to

vertical change rise is . run horizontal change

• Some students confuse the concept of slope with the plotting of ordered pairs. Since they are used to plotting points like (2, 3) by starting at the origin and moving 2 units right and 3 units 2 up, they sometimes show a slope of by moving right 2 units and up 3 units instead of 3 going up 2 and right 3 units. Answers: 1a)

5 1 8 3 3 2 ; 1b) − ; 1c) 11; 1d) − ; 1e) 0; 1f) undefined; 2a) m = , y = x+1 ; 2b) m = − , 6 3 4 4 2 3

2 3

y = − x+4; 3a) 219.49; 3b) The U.S. public debt, from 1990 to 2002, increased by about $219.49 billion per year; 4a) y = –3x + 5, –3, (0, 5), see Chapter 3 Answers for graph; 4b) y =

3 3 x − 3, , (0, –3), see Chapter 3 5 5

3 3 Answers for graph; 4c) y = − x+3, − , (0, 3), see Chapter 3 Answers for graph; 5) 43.5 million 2 2

83

Mini-Lecture 3.5 The Point-Slope Form of a Linear Equation Learning Objectives: 1. Understand the point-slope form of a linear equation. 2. Use the point-slope form to construct models from graphs. 3. Recognize parallel and perpendicular lines. 4. Key vocabulary: point-slope form of a line, parallel, perpendicular, negative reciprocal Examples: 1. Use the point-slope form to find the equation of a line with the properties given. Then write the equation in slope-intercept form. 2 a) Slope = 3, through (2, –5) b) Slope = − , through (–4, 5) 3 c) Through (8, –5) and (–5,4) d) Through (–6, 3) and (4, 3)

2. Kathy is making fixed monthly payments to her rich brother to pay back a loan that allowed her to have a swimming pool installed in her backyard. After three months, Kathy owed $6800 and after seven months, she still owed $5200. a) Using ordered pairs of the form (x, y) write a linear equation for Kathy’s balance (y) after x months. b) Using the function from part (a), determine Kathy’s balance after 12 months. c) Using the function from part (a), determine how many months it will take until her loan is paid off with a balance of $0. 3. Two points on l1 and two points on l2 are given. Determine whether l1 and l2 are parallel, perpendicular or neither. a) l1 : (9, 19) and (–2, –3); l2 : (4, 13) and (–5, –5) b) l1 : (5, –5) and (10, –2); l2 : (3, –11) and (–3, –1) 4. Find the equation of a line with the given properties. Write your answer in slope-intercept form. a) Parallel to 3x + 2 y = 7 and has a y-intercept of (0, 9). 1 b) Through (4, 3) and perpendicular to y = − x + 5. 2 Teaching Notes: • When given the coordinates of a point on a line, it is common for a student to think that the y-intercept of the line is the y-coordinate of the point given, regardless of the corresponding x-value. Mention to students that the only time this shortcut works is when the corresponding x-coordinate is 0. • Show students that when given two points on a line, it does not matter which ordered pair they choose to substitute into the point-slope form.

2 7 9 7 Answers: 1a) y = 3x − 11 ; 1b) y = − x + ; 1c) y = − x + ; 1d) y = 3 ; 3 3 13 13 2a) y = −400x + 8000 ; 2b) $3200; 2c) 20 months; 3a) parallel; 3b) perpendicular; 3 4a) y = − x + 9 ; 4b) y = 2x − 5 2 84

Mini-Lecture 3.6 The Algebra of Functions Learning Objectives:

1. Find the sum, difference, product and quotient of functions. 2. Graph the sum of functions. 3. Key vocabulary: sum of functions, difference of functions, product of functions, quotient of functions Examples:

1. If f ( x) = x − 4 and g ( x) = x 2 + 2 x − 1, find a) ( f + g )( x) b) ( f − g )( x) c) ( f ⋅ g )( x)

d) ( f / g )( x)

2. If f ( x) = x 2 + 2 and g ( x) = x − 3, find a) ( f + g )(−1) b) ( g − f )(2) c) ( f ⋅ g )(1)

d) ( g / f )(4)

3. Construct a line graph, including the total, for the following data. Average monthly home phone bill Average monthly mobile phone bill

2003 2004 2005 2006 $64 $60 $62 $67 $41 $47 $56 $61

4. Construct a bar graph, similar to Example 4 from Section 3.6, for the above data. 5. Construct a stacked line graph for the data given in problem #3. Teaching Notes:

• Once again, students are often confused by function notation. For instance, some students may think that ( f + g )(5) means to add the two functions f and g, and then multiply by 5 rather than substitute 5.

Answers: 1a) x 2 + 3x − 5 ; 1b) − x 2 − x − 3 ; 1c) x3 − 2x 2 − 9x + 4 ; 1d) 2c) –6; 2d)

1 ; 3–5) see Chapter 3 Answers 18 85

x−4 ; 2a) –1; 2b) –7; x 2 + 2x − 1

Mini-Lecture 3.7 Graphing Linear Inequalities Learning Objectives:

1. Graph linear inequalities in two variables. 2. Key vocabulary: linear inequality, half plane, boundary Examples:

1. Graph each inequality. 2 b) y ≥ − x + 1 3

a) y < 2 x − 4

c) 3x + 4 y ≤ 12

Teaching Notes:

• When finished graphing linear inequalities in which the variable y is already isolated on the left side, the following guidelines can be used to double-check your solution. For inequalities involving < or ≤, shading should occur below the boundary line. For inequalities involving > or ≥, shading should occur above the boundary line.

y

Answers: 1a) −4 −2

y

1b)

y

1c)

4

4

4

2

2

2

−2

−4

2

4

x

−4 −2

−2

−4

86

2

4

x

−4 −2

−2

−4

2

4

x

Name:

Additional Exercises 3.1 1. What are the coordinates of point A?

Date: 1. ____________________________

y

x

0 A

2. Graph the point B (−3, 4) .

2. y

x

3. Name the coordinates of the points A, B, C, and D.

3. ____________________________

y

B

A

0

C

x

D

4. Graph: x − y = 5

4. y

x

5. Graph: −3 x + 4 y = −12

5. y

x

87

Additional Exercises 3.1 (cont.) 6. Graph: 8 x − 3 y = 24

Name: 6. y

x

7. Graph: y = −3 x − 3

7. y

x

8. Graph the equation 2 x + y = 2 .

8. y

x

9. Graph: 5 x − 6 y = 30

9. y

x

10. Graph: –2x + y = 6

10. y

x

88

Additional Exercises 3.1 (cont.) 11. Graph: − x − 3 y = −3

Name: 11. y

x

12. Graph: 5 x − 7 y = 35

12. y

x

13. Graph: y = −3 x + 2

13. y

x

14. Graph the equation –2x + y = 2.

14. y

x

15. Graph: 5 x − 3 y = 15

15. y

x

89

Additional Exercises 3.1 (cont.) 16. Graph: y = −1 − x

Name: 16. y

x

17. Graph: y = 2 + x

17. y

x

18. Graph: y = − x 2 + 5

18. y

x

19. Graph the data in the following table using a broken-line graph.

19. y

Number of Rigs Drilling for Oil (Monthly Averages) 1980

1982

1984

1986

2000

4000

3500

3000

x

Temperature

20. The double line graph below compares high temperatures in Honolulu and Miami in August. Use the graph below to determine the days that Honolulu’s temperature was lower than Miami’s. 93 92 91 90 89 88 87

Honolulu Miami

11 12 13 14 15 16 17 18 19 20 August

90

20. ____________________________

Name:

Additional Exercises 3.2 1. Find the domain and range for the relation graphed below.

Date: 1. ____________________________

y

0

x

{(1, − 2 ) , ( –2, 1) , ( −1, − 5)} .

2. ____________________________

3. Find the range of the relation {(2, −5), (−1, 7), (4, −5), (3, 2)} .

3. ____________________________

2. Find the domain of the relation

4. Find the range of the relation A =

{( x, y ) x

2

}

+ y 2 = 49 .

4. ____________________________

5. Determine if the relation {(0, 7), (7, 8), (0, –6)} is a function.

5. ____________________________

6. Determine if the following is a function: {( x, y ) x + y = 5}

6. ____________________________

7. Determine if the relation {(–2, 4), (–4, 4), (–1, 2)} is a function.

7. ____________________________

8. Is the relation {(5, –4), (5, 3), (3, –5)} a function?

8. ____________________________

9. Find f ( −2 ) given f ( x ) = x + 2 .

9. ____________________________

10. Given the function f ( x ) =

6 x + 3 ; find f ( −25 ) . 5

10. ____________________________

11. Find f (−2) given f ( x) = − x 2 + 5 x + 1 .

11. ____________________________

12. If P ( x ) = x 2 − 3 x − 2 , find P ( −3) .

12. ____________________________

13. The cost of a long-distance phone call from New York to Athens is defined by C ( t ) = 0.75 ( t − 1) + 1.45 , where the cost is $1.45 for the first minute and $0.75 for each additional minute. Find the cost of a 7-minute phone call.

13. ____________________________

14. The measure in degrees of an interior angle of a regular polygon 360 . Find the with n sides is given by the function f ( n ) = 180 − n measure of an interior angle of a regular decagon (10 sides).

14. ____________________________

91

Additional Exercises 3.2 (cont.) 15. The area of an equilateral triangle with sides of length s can 1 3s 2 . Find the area of an be found by the function: f ( x ) = 4 equilateral triangle with sides of length 4.5. Round answers to the nearest 0.1. 16. Determine if the relation

{( x, y ) x

2

}

+ y 2 = 1 is a function.

Name: 15. ____________________________

16. ____________________________

17. Is the relation {(5, 6), (–1, 6), (1, 6)} a function?

17. ____________________________

18. Find f ( −1) given f ( x ) = 2 x + 1 .

18. ____________________________

19. Given the function f ( x ) =

8 x + 1 ; find f ( −21) . 7

19. ____________________________

20. Find f ( 2 ) given f ( x ) = − x 3 − 2 x 2 + 28 .

20. ____________________________

92

Name:

Additional Exercises 3.3 1. Graph the linear equation by finding x- and y-intercepts. 3x + y – 3 = 0

Date: 1.

y

x

2. Graph the linear equation by finding x- and y-intercepts. –y + 2x = –2

2.

y

x

3. Graph: x = −8

3.

y

x

4. Graph: y = −7

4.

y

x

5. Graph: −3x = 12

5.

y

x

6. Graph: x = −4

6.

y

x

93

Additional Exercises 3.3 (cont.)

Name:

7. A real estate’s initial monthly salary is $800 plus 1% of the total 7. ____________________________ homes sales he has for that month. Write an equation expressing the relationship between the real estate’s monthly salary and his monthly homes sales. Then use this equation to determine his monthly salary if his total homes sales in one particular month is $680,000.

For problems 8 – 10, the annual profit, p, of a bike manufacturer can be estimated by the formula p = 18 x − 10, 000 where x is the number of bikes sold per year. 8.

Draw a graph of profits versus bikes that must be sold for up to 6000 bikes.

y

8.

x

9. Estimate the number of bikes that must be sold for the company to break even.

9. ____________________________

10. Estimate the number of bikes sold if the company has a $30,000 profit.

10. ____________________________

11. Write the linear equation y =

2 x + 5 in standard form. 3

3 12. Write the linear equation y + 2 = − ( x − 5) in standard form. 4

13.

Graph the linear equation by finding x- and y-intercepts. 3x – 2y + 6 = 0

11. ____________________________

12. ____________________________

13.

y

x

14.

Graph the linear equation by finding x- and y-intercepts. –4y – 3x = 12

14.

y

x

94

Additional Exercises 3.3 (cont.) 15.

Graph: −4 y = 4

Name: 15.

y

x

16.

Graph: 4 x = −16

16.

y

x

17. John’s salary is $1400 plus 6% commission on monthly sales. Write an equation expressing the relationship between John’s salary and his monthly sales, and use it to find his sales for the month if his salary for the month is $4000.

17. ____________________________

For problems 18 – 20, the annual profit, p, of a bike manufacturer can be estimated by the formula p = 18 x − 30, 000 where x is the number of bikes sold per year. 18.

Draw a graph of profits versus bikes that must be sold for up to 6000 bikes.

18.

y

x

19. Estimate the number of bikes that must be sold for the company to break even.

19. ____________________________

20. Estimate the number of bikes sold if the company has a $45,000 profit.

20. ____________________________

95

Name:

Additional Exercises 3.4

Date:

1. Determine the slope of the line graphed below.

1. ____________________________

y

0

x

2. Determine the slope of the line graph below.

2. ____________________________

y

0

x

3. Find the slope of the line going through the points (2, 7) and (9, 10).

3. ____________________________

4. Find the slope of the line going through the points (–4, –6) and (–9, 4).

4. ____________________________

5. Find the slope and the y-intercept of the line 9 x + 3 y = −54 .

5. ____________________________

6. Find the slope and y-intercept of 4 x − 3 y = 24 .

6. ____________________________

7. Find an equation of the line having slope 5 and y-intercept 12.

7. ____________________________

8. Find an equation of the line having slope 7 and y-intercept –3.

8. ____________________________

9. Draw the graph of a line with y-intercept 0 and slope of

5 . 2

y

9.

x

3 10. Draw the graph of a line with y-intercept 3 and slope of − . 2

y

10.

x

96

Additional Exercises 3.4 (cont.) 11. Graph: y = 4 x + 8

Name:

11.

y

x

12. Find the slope of the line going through the points (6, –5) and (–3, –1).

12. ____________________________

13. Find the slope of the line going through the points (3, 5) and (–2, 5).

13. ____________________________

14. Find the slope and the y-intercept of the line 4 x + 2 y = −24 .

14. ____________________________

15. Find the slope and y-intercept of 7 x − 4 y = 2 .

15. ____________________________

16. Find an equation of the line having slope 4 and y-intercept 5.

16. ____________________________

17. Find an equation of the line having slope –7 and y-intercept –8.

17. ____________________________

18. Draw the graph of a line with y-intercept 3 and slope of a

3 . 7

y

18.

x

3 19. Draw the graph of a line with y-intercept 2 and slope of − . 2

y

19.

x

20. Graph: y = −2 x − 6

20.

y

x

97

Name:

Additional Exercises 3.5

Date:

1. Are the two given lines parallel? (Answer yes or no.) 9 x + 2 y = −10 9 y = − x−6 2

1. ____________________________

2. Are the two given lines perpendicular? (Answer yes or no.) −8 x − 10 y = −11 −4 x + 5 y = − 2

2. ____________________________

3. Two points on line 1 are (3, 1) and (–2, –2). Two points on line 2 are (–5, 4) and (–8, 9). Determine if line 1 and line 2 are parallel lines, perpendicular lines, or neither.

3. ____________________________

4. Find an equation of the line passing through the point (2, 8) with slope m = 4 .

4. ____________________________

5. Write the equation of a line with slope –4 passing through the point (–1, 2).

5. ____________________________

6. Find an equation of the line that passes through the point (–3, 6) and is parallel to the line 2 x + y = −6 .

6. ____________________________

7. Write the equation of the line (in slope-intercept form) passing through the point (–5, –1) and perpendicular to 7 x + 6 y = 6 .

7. ____________________________

8. Are the two given lines parallel? −2 x + 3 y = 21 y = −2 x + 7

8. ____________________________

9. Are the two given lines perpendicular? 5x − y = 9 −2 x − 10 y = 3

9. ____________________________

10. Two points on line 1 are (2, –7) and (–6, –10). Two points on line 2 are (–6, 2) and (–9, 10). Determine if line 1 and line 2 are parallel lines, perpendicular lines, or neither.

10. ____________________________

11. Find an equation of the line passing through the point (–7, –2) with slope m = −5 .

11. ____________________________

12. Write the equation of a line with slope 5 passing through the point (5, –1).

12. ____________________________

13. Find an equation of the line that passes through the point (2, –5) and is parallel to the line 2 x + 3 y = 7 .

13. ____________________________

14. Write the equation of the line (in slope-intercept form) passing through the point (–1, –8) and perpendicular to 4 x − 5 y = 6 .

14. ____________________________

98

Additional Exercises 3.5 (cont.)

Name:

15. Determine if the following line is parallel to y = 3 x − 1 . 6 x − 2 y = −5

15. ____________________________

16. Are the two given lines parallel? (Answer yes or no.) 6 x + 7 y = 35 y = −6 x − 9

16. ____________________________

17. Are the two given lines perpendicular? (Answer yes or no.) 5 x − 3 y = 10 −6 x − 10 y = 4

17. ____________________________

18. Two points on line 1 are (7, 1) and (4, –3). Two points on line 2 are (–4, 0) and (–8, 3). Determine if line 1 and line 2 are parallel lines, perpendicular lines, or neither.

18. ____________________________

19. Find an equation of the line passing through the point (2, –4) with slope m = 3 .

19. ____________________________

20. Write the equation of a line with slope 7 passing through the point (7, –4).

20. ____________________________

99

Name:

Additional Exercises 3.6

Date:

⎛ f ⎞ 1. Let f ( x ) = 16 − x 2 , g ( x ) = 4 − x . Find ⎜ ⎟ ( x ) . ⎝g⎠

(f

2. Let f ( x) = x 2 + 5 x − 3, g ( x) = 3x + 7 . Find

1. ____________________________

+ g )( x ) .

2. ____________________________

⎛ f ⎞ 3. Given f ( x ) = 4 x 2 − 9 x + 3 and g ( x ) = x 3 , find ⎜ ⎟ ( x ) . ⎝g⎠

3. ____________________________

4. Given f ( x ) = x 2 + 9 x + 6 and g ( x ) = x + 6 , find

4. ____________________________

(f

+ g )( x ) .

5. Given f ( x ) = x3 and g ( x ) = 4 + 3 x , find ( g ⋅ f )( x ) .

5. ____________________________

6. Let f ( x ) = 1 − x 2 , g ( x ) = 1 − x . Find

( fg )( x ) .

6. ____________________________

7. Let f ( x ) = 9 − x 2 , g ( x ) = 3 − x . Find

(f

7. ____________________________

− g )( x ) .

⎛ f ⎞ 8. Given f ( x ) = 5 x 2 − 6 x + 5 and g ( x ) = x 4 , find ⎜ ⎟ ( x ) . ⎝g⎠

8. ____________________________

9. Given f ( x ) = x 2 + 8 x − 8 and g ( x ) = x + 9 , find

9. ____________________________

(f

+ g )( x ) .

10. Given f ( x) = x3 and g ( x) = 7 x − 4 , find ( g ⋅ f )( x ) .

10. ____________________________

11. Let f ( x ) = 4 x − 9 x 2 + 3 , g ( x ) = 2 x 2 − 3 x . Find ( f − g )( x) .

11. ____________________________

12. Let f ( x ) = 1 − x 2 , g ( x ) = 1 + x . Find

12. ____________________________

( fg )( x ) .

⎛ f ⎞ 13. Given f ( x ) = 9 x 2 − 4 x + 7 and g ( x ) = x3 , find ⎜ ⎟ ( x ) . ⎝g⎠

13. ____________________________

14. Given f ( x ) = x 2 − 2 x + 3 and g ( x ) = x − 7 , find

14. ____________________________

15. Given f ( x ) = x 3 and g ( x ) = 5 − 3 x 2 , find

(f

+ g )( x ) .

( f ⋅ g )( x ) .

15. ____________________________

⎛g⎞ 16. If f ( x ) = x + 3 and g ( x ) = x , find the domain of ⎜ ⎟ ( x ) . ⎝ f ⎠

16. ____________________________

17. If f ( x ) = x 2 and g ( x ) = 8 , find the range of

17. ____________________________

(f

+ g )( x ) .

18. If f ( x ) = −1 + 3x 2 and g ( x ) = 2 x , find the domain of 19. If f ( x ) =

x+3 and g ( x ) = −2 , find the domain of x

( f ⋅ g )( x ) .

( f ⋅ g )( x ) .

20. If f ( x ) = x and g ( x) = 2 , find the range of ( f − g )( x) .

100

18. ____________________________ 19. ____________________________ 20. ____________________________

Name:

Additional Exercises 3.7 1. Graph: y ≤ 2 x − 2

Date: 1.

y

x

2. Graph: y ≥ − x − 2

2.

y

x

3. Graph: x − 4 y < −4

3.

y

x

4. Graph: 2 x − 5 y > −10

4.

y

x

5. Graph: y ≤ 2 x − 4

5.

y

x

6. Graph: y ≤ − x + 1

6.

y

x

101

Additional Exercises 3.7 (cont.) 7. Graph: 2 x − y < −2

Name:

7.

y

x

8. Graph: 3 x − y < −3

8.

y

x

9. Graph: y ≤ 4

9.

y

x

10. Graph: y ≤ 3 x − 1

10.

y

x

11. Graph: 5 x − 4 y > −20

11.

y

x

12. Graph: x − 6 y > −6

12.

y

x

102

Additional Exercises 3.7 (cont.) 13. Graph: y > 3 x + 2

Name: 13.

y

x

14. Graph: y ≤ −4 x

14.

y

x

15. Graph: y <

y

1 x −1 3

15.

x

16. Graph: 3 x ≥ − y + 3

16.

y

x

17. Graph: 2 x < −3 y − 12

17.

y

x

18. Graph: y > 1 −

y

3 x 2

18.

x

103

Additional Exercises 3.7 (cont.) 19. Graph: 2 x + 3 y < 12

Name:

19.

y

x

20. Graph: 3 x − 2 y ≥ 12

20.

y

x

104

Name:

Chapter 3 Test Form A

Date:

1. What is another name for the rectangular coordinate system?

1. ____________________________

2. The x-axis and y-axis divide the plane into four ________. (Fill in the blank.)

2. ____________________________

Graph. 3. y = x − 2

3.

y

x

4. y = x 2 + 2

4.

y

x

5. y = x − 1

5.

y

x

Problems 6 and 7 refer to the following relation: {(–1, 4), (2, 7), (3, 6), (–1, –5)} 6. Determine if the relation is a function.

6. ____________________________

7. Give the domain and range of the function or relation.

7. ____________________________

Problems 8 and 9 refer to the following relation: y

0

x

8. Determine if the relation is a function.

8. ____________________________

9. Give the domain and range of the function or relation.

9. ____________________________

105

Chapter 3 Test Form A (cont.)

Name:

Graph each equation using the x and y intercepts. 10. y =

y

1 x +1 3

10.

x

11. 5 x − 3 y = −15

11.

y

x

12. Graph x = −4 .

12.

y

x

13. Graph y = −2 .

13.

y

x

14. Determine the slope of the line through the points (3, –2) and (7, 3).

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation 11x − 2 y = 12 .

15. ____________________________

16. Determine if the graphs of the two equations are parallel, perpendicular, or neither. Explain your answer. 2 x + y = −3 and x − 2 y = −4

16. ____________________________

17. Find the equation of the line through (–8, –1) that is 3 parallel to the graph of y = x − 4 in slope-intercept form. 2

17. ____________________________

18. Find the equation of the line through (1, –2) that is perpendicular to the graph of 6 x − 3 y = 9 in standard form.

18. ____________________________

106

Chapter 3 Test Form A (cont.)

Name:

If f ( x) = x − 3 and g ( x) = x 2 + 2 , find: 19.

(f

+ g )( −1)

19. ____________________________

20. (f · g)(2)

20. ____________________________

If f ( x ) = x 2 + x − 6 and g ( x ) = 2 x − 4 , find: 21. The domain of

(f

+ g )( x )

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

Graph each inequality. 23. y < 2 x − 2

23.

y

x

24. x ≥ −3

24.

y

x

25. The bar graph shows the percent of nitrogen in three common fertilizers. How much more nitrogen is there in 200 pounds of ( NH 4 )3 PO 4 than in 200 pounds of NaNO3 ? NaNo3

16.5%

(NH4)2SO4

21.2%

(NH4)3PO4

28.2% 0

5

10 15 20 25 30 Percent Nitrogen

107

25. ____________________________

Name:

Chapter 3 Test Form B

Date:

1. What is a relation?

1. ____________________________

2. What is the domain of a relation?

2. ____________________________

Graph. 3. y = 2 x − 3

3.

y

x

4. y = x 2 − 1

4.

y

x

5. y = x + 2

5.

y

x

Problems 6 and 7 refer to the following relation: {(2, 6), (3, 6), (4, 6), (5, 6)} 6. Determine if the relation is a function.

6. ____________________________

7. Give the domain and range of the function or relation.

7. ____________________________

Problems 8 and 9 refer to the following relation: Age Paul

31

Dan

35

Doyle

8. Determine if the relation is a function.

8. ____________________________

9. Give the domain and range of the function or relation.

9. ____________________________

108

Chapter 3 Test Form B (cont.)

Name:

Graph each equation using the x and y intercepts. 10. y =

y

−4 x+4 5

10.

x

11. 3x + y = 0

11.

y

x

12. Graph x = −6 .

12.

y

x

13. Graph y = 5.

13.

y

x

14. Determine the slope of the line through the points (–1, 7) and (4, 8).

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation 4 x + 5 y = −4 .

15. ____________________________

16. Determine if the graphs of the two equations are parallel, perpendicular, or neither. 3 x − 5 y = −5 and 5 x − 3 y = 6

16. ____________________________

17. Find an equation of the line through (3, 2) that is parallel to the line through (2 ,5) and (–1, –1).

17. ____________________________

18. Find the equation of the line through (1, –4) that is perpendicular to the graph of 2 x − 3 y = 5 in standard form.

18. ____________________________

109

Chapter 3 Test Form B (cont.)

Name:

If f ( x ) = 7 x − 2 and g ( x ) = − x 2 , find: 19.

(f

+ g )(1)

19. ____________________________

⎛ f ⎞ 20. ⎜ ⎟ ( 0 ) ⎝g⎠

20. ____________________________

If f ( x ) = x 2 + 2 x and g ( x ) = 3 x − 9 , find: 21. The domain of

(f

+ g )( x )

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

Graph each inequality. y

1 23. y ≥ − x − 2 2

23.

x

24. x < 4

24.

y

x

25. The bar graph shows the percent of nitrogen in three common fertilizers. How much more nitrogen is there in 400 pounds of ( NH 4 )3 PO 4 than in 400 pounds of ( NH 4 )2 SO4 ? NaNo3

16.5%

(NH4)2SO4

21.2%

(NH4)3PO4

28.2% 0

5

10 15 20 25 30 Percent Nitrogen

110

25. _____________________________

Name:

Chapter 3 Test Form C

Date:

1. What is a function?

1. ____________________________

2. Does x usually represent the dependent variable, or the independent variable?

2. ____________________________

Graph. 3. y = 3 x − 2

3.

y

x

4. y = x3 − 1

4.

y

x

5. y = − x

5.

y

x

Problems 6 and 7 refer to the following relation: {(2, 5), (–2, 3), (1, 5), (0, –1)} 6. Determine if the relation is a function.

6. ____________________________

7. Give the domain and range of the function or relation.

7. ____________________________

Problems 8 and 9 refer to the following relation: y

0

x

8. Determine if the relation is a function.

8. ____________________________

9. Give the domain and range of the function or relation.

9. ____________________________

111

Chapter 3 Test Form C (cont.)

Name:

Graph each equation using the x- and y-intercepts. 10. y = −2 x + 4

10.

y

x

11. x − 6 y = 6

11.

y

x

12. Graph x = 0 .

12.

y

x

13. Graph y = 0 .

13.

y

x

14. Determine the slope of the line through the points (–2, –1) and (0, 7).

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation −4 x − 3 y = 7 .

15. ____________________________

16. Determine if the graphs of the two equations are parallel, perpendicular, or neither. Explain your answer. x + 2 y = 16 and x + 2 y = −10

16. ____________________________

17. Find the equation of the line through (–4, 0) that is parallel to the graph of y = −3 x + 6 in slope-intercept form.

17. ____________________________

18. Find the equation of the line through (–7, –1) that is perpendicular to the graph of x − y = 3 in standard form.

18. ____________________________

112

Chapter 3 Test Form C (cont.)

Name:

If f ( x) = x − 11 and g ( x) = 2 x 2 − 4 , find: 19.

(f

− g )( −1)

19. ____________________________

20. (f · g)(–1)

If f ( x ) =

20. ____________________________

1 x + 2 and g ( x ) = x 2 − 1 , find: 2

21. The domain of (f · g)(x)

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

Graph each inequality. 23. y ≤ 3

23.

y

x

24. y > −3 x − 2

24.

y

x

Rainfall (mm)

25. The graph shows the monthly mean rainfall for Fort Ogelthorpe. 100 90 80 70 60 50 0

y

x J

F M A M J Month

J

Between which two months did the monthly mean rainfall increase the most?

113

25. ____________________________

Name:

Chapter 3 Test Form D

Date:

1. Does y usually represent the dependent variable or the independent variable?

1. ____________________________

2. Describe the vertical line test.

2. ____________________________

Graph. 3. y = −2 x + 1

3.

y

x

4. y = − x 3 + 1

4.

y

x

5. y = − x + 1

5.

y

x

Problems 6 and 7 refer to the following relation: {(–4, 0), (–3, 2), (–2, 4), (–3, 6)} 6. Determine if the relation is a function.

6. ____________________________

7. Give the domain and range of the function or relation.

7. ____________________________

Problems 8 and 9 refer to the following relation: Lunch Sam

Bagel

Will

Pasta

Rita

Grapes

8. Determine if the relation is a function.

8. ____________________________

9. Give the domain and range of the function or relation.

9. ____________________________

114

Chapter 3 Test Form D (cont.)

Name:

Graph each equation using the x- and y-intercepts. 10. y = x + 5

10.

y

x

11. 3x − 2 y = 6

11.

y

x

12. Graph x = −4 .

12.

y

x

13. Graph y = 7 .

13.

y

x

14. Determine the slope of the line through the points (0, 5) and (3, 1).

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation 7 x + 9 y = 10 .

15. ____________________________

16. Determine if the graphs of the two equations are parallel, perpendicular, or neither. Explain your answer. 2 x − 5 y = 5 and 5 x + 2 y = −2

16. ____________________________

17. Find the equation of the line through (3, 0) that is parallel to the graph of y = 2 x + 1 in slope-intercept form.

17. ____________________________

18. Find the equation of the line through (0, 4) that is perpendicular to the graph of y = 13 x + 8 in standard form.

18. ____________________________

115

Chapter 3 Test Form D (cont.)

Name:

If f ( x) = 12 x + 4 and g ( x) = 3 − x 2 , find: 19. (f · g)(4)

19. ____________________________

(f

20. ____________________________

20.

+ g ) (−2)

If f ( x) = 2 x + 5 and g ( x) = x 2 − 9 , to find: 21. The domain of

(f

+ g )( x )

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

Graph each inequality. 23. y ≤ 5

23.

y

x

y

1 24. y > − x + 2 3

24.

x

Rainfall

25. The double line graph below compares rainfall in inches in Oregon and Washington in March 1993. Use the graph to determine the combined rainfall on March 7th. 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Oregon Washington

1 2 3 4 5 6 7 8 9 10 March

116

25. ____________________________

Name:

Chapter 3 Test Form E

Date:

1. True or False: If a horizontal line intersects a graph more than once, the graph is not a function.

1. ____________________________

2. Write the equation y = 2 x − 7 in function notation.

2. ____________________________

Graph. 3. y =

y

1 x +1 2

3.

x

4. y = − x 2 − 1

4.

y

x

5. y = − x + 2

5.

y

x

Problems 6 and 7 refer to the following relation: {(8, –2), (6, –3), (4, –4), (2, –5)} 6. Determine if the relation is a function.

6. ____________________________

7. Give the domain and range of the function or relation.

7. ____________________________

Problems 8 and 9 refer to the following relation: y

0

x

8. Determine if the relation is a function.

8. ____________________________

9. Give the domain and range of the function or relation.

9. ____________________________

117

Chapter 3 Test Form E (cont.)

Name:

Graph each equation using the x- and y-intercepts. y

3 10. y = − x + 3 4

10.

x

11. 5 x − 2 y = −10

11.

y

x

12. Graph x = 8 .

12.

y

x

13. Graph y = 7 . y = −8

13.

y

x

14. Determine the slope of the line through the points ( 32 , 4 ) and ( − 73 , −1) .

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation 7 x + 2 y = 8 .

15. ____________________________

16. Determine if the graphs of the two equations are parallel, perpendicular, or neither. Explain your answer. −2 5 3 y= x + and y = x − 7 3 3 2

16. ____________________________

17. Find the equation of the line through (5, –3) that is parallel to the graph of y = 6 x − 8 in slope-intercept form.

17. ____________________________

18. Find the equation of the line through (–3, 4) that is perpendicular to the graph of 9 x − 3 y = −12 in standard form.

18. ____________________________

118

Chapter 3 Test Form E (cont.)

Name:

If f ( x ) = 6 x − 12 and g ( x ) = x 2 − 1 , find: 19.

(f

− g ) (2)

19. ____________________________

20.

( f ⋅ g ) (−2)

20. ____________________________

If f ( x ) = x 2 − 2 x + 7 and g ( x ) = x , find: 21. The domain of (f · g)(x)

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

Graph each inequality. 23. x < −3

23.

y

x

24. y ≥ 2 x − 5

24.

y

x

Rainfall

25. The double line graph below compares rainfall in inches in Oregon and Washington in March 1993. Use the graph to determine which state had the most rain on March 4th. 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Oregon Washington

1 2 3 4 5 6 7 8 9 10 March

119

25. ____________________________

Name:

Chapter 3 Test Form F

Date:

1. Name the test used to determine whether a graph represents a function?

1. ____________________________

2. True or false? To find the y-intercept of a function, you set x-value equal to 0 and solve for y.

2. ____________________________

3. Determine an equation for the given graph.

3. ____________________________

y

x

0

4. Determine the range.

4. ____________________________

y

x

0

5. Determine the domain.

5. ____________________________

y

x

0

For problems 6 and 7, determine an equation for the given graph. 6.

y

0

7.

6. ____________________________

x

y

0

7. ____________________________

x

120

Chapter 3 Test Form F (cont.)

Name:

8. Determine if

{( 0,1) , (1, 2 ) , ( 2,3) , (1, 4 )} is a function.

8. ____________________________

9. Determine if

{( 9, 0 ) , (10, 0 ) , (11, 0 ) , (12, 0 )} is a function.

9. ____________________________

10. Determine the domain and range of y = x + 1 .

11. Determine the domain and range of y =

10. ____________________________

1 . x

11. ____________________________

Determine the x- and y-intercepts of each equation: 12. 5 x − y = 3

13. y =

12. ____________________________

1 x+4 2

13. ____________________________

14. Determine the slope of the line through the points ( −2, 4 ) and ( −6, 12 ) .

14. ____________________________

15. Determine the slope and y-intercept of the graph of the equation 5x − 4 y = 7 .

15. ____________________________

16. Determine if these two equations have graphs that are perpendicular. y = 2 x + 3; y = −2 x − 6

16. ____________________________

17. Find the equation of the line through ( −4, 3) that is parallel to the

graph of y =

17. ____________________________

2 x − 5 in slope-intercept form. 3

18. Find the equation of the line through ( 0, 2 ) that is perpendicular to the graph of 4 x − 2 y = 8 in standard form.

18. ____________________________

If f ( x ) = 3x − 1 and g ( x ) = x 2 − 2 , find: 19.

(f

+ g )( −1)

19. ____________________________

⎛ f ⎞ 20. ⎜ ⎟ (1) ⎝g⎠

20. ____________________________

121

Chapter 3 Test Form F (cont.)

Name:

If f ( x ) = 2 x − 11 and g ( x ) = x 2 − 4 , find: 21. The domain of ( f ⋅ g )( x )

21. ____________________________

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

22. ____________________________

For problems 23–24, determine an inequality that describes the given graph. y

23.

0

23. ____________________________

x

y

24.

0

24. ____________________________

x

Rainfall (mm)

25. The graph shows the monthly mean rainfall for Fort McCoy. 100 90 80 70 60 50 0

25. ____________________________

y

x J

F M A M J Month

J

Between which two months did the monthly mean rainfall increase the most?

122

Name:

Chapter 3 Test Form G

Date:

1. Which of the following is true for a function? (a) each y value corresponds to exactly one x value (c) each y value corresponds to more than one x value

(b) each x value corresponds to exactly one y value (d) each x value corresponds to more than one y value

2. Which is the standard form of a linear equation? (b) y − y0 = m ( x − x0 )

(a) y = mx + b

(c) ax + by = c

(d) ay + bx = c

For problems 3–7, determine which equation describes the given graph. 3.

y

x

0

(a) y = 3 x − 6 4.

1

(d) y = −6 x − 2

(b) y = − x 2

(c) y = x3

(d) y = − x 3

(b) y = − x − 5

(c) y = − x + 5

(d) y = − x − 5

(b) x = 2

(c) y = 2 x

(d) y =

x

(a) y = x 2 y

0

x

(a) y = x + 5 6.

(c) y = −6 x + 2

y

2 0

5.

(b) y = 3x + 6

y

0

(a) y = 2

x

123

1 x 2

Chapter 3 Test Form G (cont.) 7.

Name:

y

x

0

(a) y = −4

(b) x = −4

(c) y = −4 x

1 (d) y = − x 4

8. Determine which of the following relations is a function. (a) {(1, 2), (–1, 2), (1, 3), (–1, 3)} (c) {(0, 1), (0, 2), (0, 3), (0, 4)}

(b) {(1, 2), (–1, 2), (–3, 2), (1, 0)} (d) {(1, 0), (2, 0), (3, 0), (4, 0)}

9. Determine which of the following relations is a function. (a) {(1, 7), (2, 7), (3, 7), (4, 7)} (c) both are functions

(b) {(2, 3), (3, 4), (5, 6), (7, 8)} (d) neither are functions

1 10. Determine the domain and range of y = − x − 2 . 2

⎧ 1⎫ (b) D: ⎨ x x > − ⎬ , R: R 2⎭ ⎩ ⎧ 1⎫ (d) D: R, R: ⎨ y y ≥ − ⎬ 2⎭ ⎩

(a) D: R, R: R ⎧ 1⎫ (c) D: ⎨ x x ≤ − ⎬ , R: R 2⎭ ⎩

11. Determine the domain and range of y = x − 1 . (a) D: R, R: { y y ≤ −1}

(b) D: R, R: { y y ≥ −1}

(c) D: { x x ≤ −1} , R: R

(d) D: { x x ≥ −1} , R: R

For problems 12 – 13, determine the slope and y-intercept of each equation: 12. 3x − 6 y = −9 (a) slope =

1 ; y-intercept 2

⎛ 3⎞ ⎜ 0, ⎟ ⎝ 2⎠

3⎞ ⎛ ⎜ 0, − ⎟ 2⎠ ⎝ ⎛ 3⎞ (d) slope = 3; y-intercept ⎜ 0, ⎟ ⎝ 2⎠ 1 (b) slope = − ; y-intercept 2

(c) slope = 3; y-intercept (0, –9) 13. y = 4 x − 8 1 (a) slope = − ; y-intercept (0, –8) 4 (c) slope = –4; y-intercept (0, –8)

1 ; y-intercept (0, –8) 4 (d) slope = 4; y-intercept (0, –8)

(b) slope =

124

Chapter 3 Test Form G (cont.)

Name:

14. Determine the slope of the line through the points ( 3, 7 ) and ( −2, − 3) . (a) –4

(b) –2

(c) 2

(d) 4

15. Determine the slope and y-intercept of the graph of the equation x − 3 y = −6 . 1 ; y-intercept (0, 2) 3 (c) slope = 1; y-intercept ( 0, 6 )

1 ; y-intercept (0, –2) 3 (d) slope = 1; y-intercept ( 0, − 2 )

(b)slope =

(a) slope =

16. Determine which two equations have graphs that are parallel. (a) y = 2 x + 3; y = 2 x − 5 (c) y = 2 x + 3; y +

(b) y = 2 x + 3; y = −2 x − 5

1 x=5 2

1 (d) y = 2 x + 3; y = − x + 3 2

17. Find the equation of the line through ( 0,3) that is parallel to the graph of y = −2 x − 7 in slope-intercept form. (a) y = 3 x − 7

(b) y = −2 x + 3

(c) y = 12 x + 3

(d) y = 12 x − 7

18. Find the equation of the line through (5, –2) that is perpendicular to the graph of 8 x − 2 y = 4 in standard form. 1 5 (a) y = − x + 4 4

1 3 (b) y = − x − 4 4

(c) x + 4 y = 5

(d) x + 4 y = −3

(b) 3

(c) 2

(d) 5

(b) 1.5

(c) 3

(d) undefined

For problems 19 – 20, if f ( x) = 3 x and g ( x) = 2 − x 2 , find: 19. ( f + g )(3) (a) 9

⎛f ⎞ 20. ⎜ ⎟ ( 0 ) ⎝g⎠ (a) 0

For problems 21 – 22, if f ( x ) = 3 x 2 + 1 and g ( x ) = x 2 − 9 , find: 21. The domain of

(f

+ g )( x )

(a) R

(b)

{ x x ≠ 3}

(c)

{ x x ≠ ±3}

(d)

{ x x ≠ 9}

(b)

{ x x ≠ 3}

(c)

{ x x ≠ ±3}

(d)

{ x x ≠ 9}

⎛f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠ (a) R

125

Chapter 3 Test Form G (cont.)

Name:

For problems 23–24, determine which inequality describes the given graph. y

23.

0

x

(a) x ≥ 2

(b) x > 2

(c) y ≥ 2

(d) y > 2

(b) y > 3x

(c) y ≥ −3x

(d) y > −3 x

y

24.

0

(a) y ≥ 3 x

x

Temperature

25. The double line graph below compares high temperatures in Honolulu and Miami in August. From the days listed, use the graph below to determine the day that Honolulu’s temperature was the same as Miami’s. 93 92 91 90 89 88 87

Honolulu Miami

11 12 13 14 15 16 17 18 19 20 August

(a) August 15

(b) August 19

(c) August 16

126

(d) August 18

Name:

Chapter 3 Test Form H

Date:

1. The point where the graph crosses the x-axis is called (a) the x-intercept

(b) the y-intercept

(c) the origin

(d) the slope

2. To find the x-intercept of an equation, you (a) set y = 0 and solve for x (c) set x = 0 and y = 0 and solve for the slope

(b) set x = 0 and solve for y (d) use the vertical line test

For problems 3–7, determine which equation describes the given graph. y

3.

0

x

(a) y = 2 x − 2

0

(a) y =

1 x−2 2

(d) y =

1 x+4 2

x

1 x

(b) y = −

1 x

(c) y = x3

(d) y = − x 3

(b) y = − x − 4

(c) y = − x + 4

(d) y = x − 4

(b) x = 2

(c) y = −2

(d) y = 2

y

0

x

(a) y = x + 4 6.

(c) y =

y

4.

5.

(b) y = 2 x + 4

y

0

(a) x = −2

x

127

Chapter 3 Test Form H (cont.)

Name:

y

7.

0

x

(a) x = 3

(b) x = −3

(c) y = 3

(d) y = −3

8. Determine which of the following relations is a function. (a) {(2, –1), (2, 0), (3, –1), (3, 0)} (c) {(2, –1), (0, 2), (3, –1), (2, 4)}

(b) {(2. –1), (0, 2), (3, –1), (0, 3)} (d) {(2, –1), (0, 2), (3, –1), (4, 2)}

9. Determine which of the following relations is a function. (a) {(1, 4), (2, 4), (3, 4), (4, 4)} (c) {(4, 1), (4, 2), (4, 3), (4, 4)}

(b) {(1, 4), (2, –4), (3, 0), (1, 5)} (d) none of these are functions

10. Determine the domain and range of y = x 2 . (a) D: R, R: R

(b) D: R, R: { y y ≤ 0}

(c) D: R, R: { y y ≥ 0}

(d) D: { x x ≥ 0} , R: R

11. Determine the domain and range of y = x + 3 . (a) D: R, R: R

(b) D: R, R: { y y > 3}

(c) D: R, R: { y y ≥ 3}

(d) D: { x x ≥ 3} , R: R

For problems 12 – 13, determine the x- and y-intercepts of each equation: 12. y = 12 x + 11 (a)

(11, 0 ) ; ( 0, 12 )

(b)

( 12 , 0 ) ; ( 0, − 112 )

(c)

( −22, 0 ) ; ( 0,11)

(d)

( 112 , 0 ) ; ( 0,11)

(c)

( −6, 0 ) ; ( 0, − 3)

(d)

( 6, 0 ) ; ( 0, − 3)

13. 5 x − 10 y = 30 ⎛1 ⎞ (a) ⎜ , 0 ⎟ ; ( 0, 30 ) ⎝2 ⎠

⎛ 1 ⎞ (b) ⎜ − , 0 ⎟ ; ( 0, 30 ) ⎝ 2 ⎠

14. Determine the slope of the line through the points ( −7, −11) and ( 2, 7 ) . (a) −

1 2

(b)

1 2

(c) –2

128

(d) 2

Chapter 3 Test Form H (cont.)

Name:

15. Determine the slope and y-intercept of the graph of the equation x − 10 y = 5 . ⎛ (b) slope = 1; y-intercept ⎜ 0, ⎝ 1 (d) slope = − ; y-intercept 10

(a) slope = 1; y-intercept (0, 5) (c) slope =

1 ; y-intercept 10

1⎞ ⎛ ⎜ 0, − ⎟ 2⎠ ⎝

1⎞ − ⎟ 2⎠ ⎛ 1⎞ ⎜ 0, ⎟ ⎝ 2⎠

16. Determine which two equations have graphs that are perpendicular. (a) y = 3x + 2; y = 3 x − 7 (c) y = 3x + 2; y =

(b) y = 3x + 2; y = −3x − 7

1 x−7 3

1 (d) y = 3x + 2; y = − x − 7 3

17. Find the equation of the line through (–4, –4) that is parallel to the graph of y = 2 x + 9 in slope-intercept form. (a) y = 2 x + 4

(b) y = 2 x + 8

(c) y = 2 x − 4

1 (d) y = − x + 4 2

18. Find the equation of the line through (7, 7) that is perpendicular to the graph of 2 x − y = 3 in standard form. (a) x + 2 y = 7

(b) x + 2 y = 21

(c) 2 x − y = 7

(d) 2 x − y = −7

For problems 19 – 20, if f ( x ) = x 2 + x − 3 and g ( x ) = x 2 − 16 , find: 19.

(f

− g )( 0 )

(a) –19

(b) –13

(c) 13

(d) 19

(c) –15

(d) undefined

⎛ f ⎞ 20. ⎜ ⎟ ( −4 ) ⎝g⎠

(b) −

(a) 15

15 12

For problems 21 – 22, if f ( x ) = x 3 + 2 x 2 − 1 and g ( x ) = x 3 − 1 , find: 21. The domain of

( f D g )( x )

(a) R

(b)

{ x x ≠ 1}

(c)

{ x x ≠ ±1}

(d)

{ x x ≥ −1}

(b)

{ x x ≠ 1}

(c)

{ x x ≠ ±1}

(d)

{ x x > −1}

⎛ f ⎞ 22. The domain of ⎜ ⎟ ( x ) ⎝g⎠

(a) R

129

Chapter 3 Test Form H (cont.)

Name:

For problems 23–24, determine which inequality describes the given graph. y

23.

x

0

(a) y < 7

(b) y ≤ 7

(c) x < 7

(d) x ≤ 7

(b) y ≤ −3 x + 6

(c) y < 3 x + 6

(d) y ≤ 3 x + 6

y

24.

x

0

(a) y < −3 x + 6

Number of Rigs Drilling for Oil

25. What is the combined monthly average number of rigs drilling for oil for the years 1982 and 1984? 4000

y

3000 2000 1000 x 1980 1982 1984 1986 Monthly Averages

(a) 4000

(b) 4500

(c) 5500

130

(d) 7000