Chap 2 Test Answers

A2_3eTE02_CR_109-113

10/14/05

2:07 PM

Page 112

Chapter

2

2

Chapter Test

Chapter Test

Find the domain and range. Graph each relation.

• • •

For each direct variation, find the constant of variation. Then find the value of y when x ≠ –0.5.

1. {(0, 0), (1, -1), (2, -4), (3, -9), (4, -16)} 1–2. See back of book. 2. {(3, 2), (4, 3), (5, 4), (6, 5), (7, 6)}

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• •

3. Domain
2 1 3 4 12

4. Domain 1
12 2 3 3 10 4 5 5 3–4. See margin. Suppose f(x) ≠ 2x – 5 and g(x) ≠ »–3x – each value. Range

5. f(3) 1

6. f(1) + g(2) 4

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24. y = 4 when x = 0.5 25. y = 2 when x = 3 2 1 8; –4 3 , 23 26. Transportation The number of minutes a freight train takes to pass an intersection varies directly with the number of cars in the train. A 150-car train passes in 3 min. How long will a 210-car train take to pass? 4.2 min

Range

1
100

0 2 12

1…. Find

Graph each function. 27–30. See back of book.

7. g(0) 1

8. g(2) - f(0) 9. f(-1) - g(3) 10. 2g(-4) 22 12 –17 11. Open-Ended Graph a relation that is not a function. Find its domain and range. Check students’ work. Find the slope of each line.

27. y = 3x + 4

28. y = ∆5x - 3« + 1

29. y = -∆x - 3« + 1

30. y = 3 - 25 x

31. Recreation The table displays the amounts the Jackson family spent on vacations during the years 1996–2006. Jackson Family Vacation Costs

12. through (3, 5) and (1, 1) 2 13. 4x + 3y =

2 243

14. through (-0.5, 0.5), perpendicular to y = -2x - 4 Write in standard form an equation of the line with the given slope through the given point. 2x – 5y ≠ –23 3x ± y ≠ 0 15. slope = -3, (0, 0) 16. slope = 25 , (6, 7)

L2

Adapted Chapter Test Chapter Test Name

Class

L3

Date

Chapter Test

Form A

Chapter 2 Find the domain and range of each relation, and determine whether it is a function.

1. {(2, 1), (-4, 5), (1, 7), (2, -3), (-1, 2)}

2. {(1, -1), (2, -2), (3, -3), (4, -4), (5, -5)}

3.

4.

y

y

2

2 x

2

O

x 2

2

O

2

2

5. Draw a mapping diagram for the relation {(-3, 2), (-1, 0), (1, 2), (3, 4)}. Is the relation a function? Explain. Suppose f(x) ≠ 3x – 4 and g(x) ≠ »x… ± 3. Find each value.

7. fa 31 b 1 g(22)

6. ƒ(2)

8.

f(1) g(1)

Find the constant of variation for each direct variation. Then find the value of y when x ≠ 34.

10. y 5 32 when x 5 41

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9. y = 2 when x = 6

11. The diameter of a tree varies directly as its age. A 15-year old tree is 3.75 in. in diameter. How old will the tree be when it is 25 in. in diameter? Find the slope of each line.

12. 3x - 5y = 15

13. through (-2, 7) and (4, 1)

14. through (6, 1) and perpendicular to y 5 23 x 1 41 Graph each function.

15. y 5 21 x 1 1

16. y = ∆x + 2« - 3

17. y = -∆x« + 4

18. y = 3 - 2x

Write in standard form the equation of the line with the given slope through the given point.

19. slope = 6; a 12 , 2b

20. slope = 41 ; (4, 3)

17. slope = 4, (-2, -5) 18. slope = -0.5, (0, 6) x ± 2y ≠ 12 4x – y ≠ –3 Write in point-slope form an equation of the line through each pair of points. Answers may vary. Samples: 19. (0, 0) and (-4, 7) 7 20. (-1, -6) and (-2, 10) y ± 6 ≠ –16(x ± 1) y 5 24x 21. (3, 0) and (-1, -2) 22. (9, 5) and (8, 2) y – 2 ≠ 3(x – 8) y 5 12 (x 2 3) 23. a. Open-Ended Write an equation of a line with negative slope. a–e. See back of book. b. Write an equation of the line perpendicular to the line from part (a) passing through (-6, 9). c. Write an equation of the line parallel to the line from part (b) passing through (12, 12). d. Write an equation of the line perpendicular to the line from part (c) passing through (-1, -4). e. Graph the lines from parts (a), (b), (c), and (d). If they form a polygon, describe it.

21. slope = -2; (0, 0)

1 2

Year

Cost

Year

Cost

1996 1997 1998 1999 2000 2001

$1000 $1750 $1750 $2000 $2200 $2700

2002 2003 2004 2005 2006

$2750 $3200 $2900 $3100 $3300

a–c. See back of book. a. Make a scatter plot of the data. b. Draw a trend line. Write its equation. c. Estimate the cost to the Jackson family of vacations in 2008. d. Writing Explain how to use a trend line with a scatter plot. Check students’ work. Describe each transformation. Then, graph 32–37. See back of book. each function. 32. y = ∆x« - 4

33. y = ∆x - 1« - 5

34. y = -∆x + 4« + 3

35. y = 2∆x + 1«

36. y = ∆x« + 5

37. y = -12 ∆x + 2« - 3

Graph each inequality. 38–41. See back of book. 38. y $ x + 7

39. y . ∆2x + 3« - 3

40. 4x + 3y , 2

41. y # -∆x + 1« - 2

Write in slope-intercept form the equation of the line through each pair of points.

22. (0, 0) and (-2, 3)

23. (1, 5) and (-3, 3)

24. (-4, 1) and (-2, -2)

112 Algebra 2 Chapter 2

Form A Test

Chapter 2 Chapter Test

27

page 112 Chapter Test 1 3. domain: e 22, 1, 3, 42r ,

1 4. domain: e 22, 0.3, 5 f ,

y 4

range: {–0.01, 0, 2.5}

2

range: {1, 2, 3, 4, 5}

x 2 O

112

2

4

y 1 O 1 1

x 3