Precalc Test Review 2

TEST REVIEW PRECALCULUS Name___________________________________

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. Graph the pair of functions on the same plane. Use a dashed line for g(x). 1) f(x) = x3 , g(x) = (x + 5)3

2) f(x) = x , g(x) = -2 x

1)

2)

1

3) f(x) = x , g(x) =

1 x+6 -4 3

3)

Write the equation of the graph after the indicated transformation(s). 4) The graph of y = x is translated 9 units to the right.

5) The graph of y = x2 is translated 4 units to the left and 5 units downward.

4)

5)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 6) The graph of y = x is reflected across the y-axis. This graph is then vertically stretched by a factor of 8.4. Finally, the graph is shifted 3 units downward. A) f(x) = 8.4 -x - 3 B) f(x) = 3 -x - 8.4 C) f(x) = 8.4 -x + 3 D) f(x) = -8.4 x - 3

2

6)

7) The graph of y = x is vertically stretched by a factor of 2.4. This graph is then reflected across the x-axis. Finally, the graph is shifted 0.32 units downward. A) f(x) = -2.4 x - 0.32 B) f(x) = 2.4 -x - 0.32 C) f(x) = 2.4 x - 0.32 D) f(x) = 2.4 x - 0.32

Determine whether the function is even, odd, or neither. 8) f(x) = 2x 2 + 4 A) Odd

B) Even

9) f(x) = -8x3 + 3x A) Neither

10) f(x) = -2x4 + 4x - 3 A) Odd

C) Neither

B) Odd

C) Even

B) Neither

C) Even

Write an inequality whose solution set is the interval. 11) (-5, 1) A) -5 < x < 1 B) -5 < x > 1

12) (1, ) A) x

1

C) -5

B) x < 1

C) x

3

x

1

1

7)

8)

9)

10)

D) -5 > x > 1

D) x > 1

11)

12)

Write the solution set in interval notation. 5 13) x A) (- , 5) B) (- ,

13) 5]

C) [ 5, )

Solve the inequality. Write the solution set using interval notation and graph it. 14) -4(6x + 14) < -28x - 32

A) (-28, )

B) (6, )

C) (- , -28)

D) (- , 6)

4

D) ( 5, )

14)

Solve the inequality by reading the graph. 15) 4x - 3 2x + 1

y = 2x + 1 A) [2, )

y = 4x-3

15)

B) (- , 2]

C) (- , 2)

D) (2, )

Solve the compound inequality. Write the solution set using interval notation and graph it. 16) -7 < -3x + 2 5

A) [-3, 1)

B) (-1, 3]

C) (-3, 1]

D) [-1, 3)

5

16)

x+1 2

17) -1

3

17)

A) (-7, 1)

B) [-3, 5]

C) [-5, 3]

D) [-1, 7]

Solve the absolute value inequality. Write the solution set using interval notation. 18) b - 8 - 9 > 2 A) (- , -3) (1, ) B) (- , -3) (19, ) C) (- , -1) (3, ) D) (-3, 19)

19) |17x - 8| < -3 5 A) - , 17

18)

19)

11 , 17

B) (- , )

C)

D)

5 11 , 17 17

Find the real or imaginary solutions by using the quadratic formula. 20) 3n2 = -8n - 2 A)

-4 ± 10 3

B)

-8 ± 10 3

C)

6

-4 ± 22 3

20) D)

-4 ± 10 6

21) x2 = 9 - 4x A) {-2 ± i 13}

21) B) {-1 ±

13}

C) {2 +

13}

D) {-2 ±

13}

Find the solutions to the equation by reading the graph. 22) 2x2 - 5x - 3 = 0

22)

y = 2x2 - 5x - 3

A) -3, -

1 ,0 2

B) -

1 ,0 2

C) -

1 ,3 2

D) 0, -3

Use the method of your choice to find all real solutions of the equation. x+6 x-8 = 23) x-7 x+4 A) -

4 4 , 5 5

B)

C) {-6, -4, 7, 8}

23) D)

32 25

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. Solve the inequality. State the solution set in interval notation. 24) x2 - 3x - 18 < 0

7

24)

25) x2 + 10x + 21 > 0

25)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the vertical line test to determine whether y is a function of x. 26)

A) Yes

26)

B) No

Determine whether the relation is a function. 27) {(-7, -5), (-7, 8), (-1, -4), (4, 7), (10, 3)} A) Yes

B) No

28) {(-4, -2), (-2, 4), (3, -6), (8, -3)} A) Yes

B) No

8

27)

28)

Evaluate. 29) Find g(a + 1) when g(x) = A)

1 a+1 2

1 x + 1. 2

B)

29)

a+3 2

C)

a-3 2

D)

1 a-2 2

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. Give the domain and range of the relation. 30)

30)

31)

31)

9

Find the domain and range. 32) y = 9 + x

32)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of y = f(x) is given. Use the graph to find the function value. 33) Find f(4).

33)

10

10

-10

-10

A) 6

B) 0

C) -8

10

D) 4

OPEN ENDED QUESTIONS. Answer the following questions and show all necessary work to receive full credit. Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 34) 34)

35)

35)

11

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a function f is given. Use the graph to answer the question. 36) For what numbers x is f(x) > 0?

36)

100

100

-100

-100

A) [-100, -60), (70, 100) C) (- -60)

B) (-60, 70) D) (-60, )

37) How often does the line y = 20 intersect the graph?

37)

100

100

-100

-100

A) once C) three times

B) twice D) does not intersect

12

Answer the question about the given function. x2 - 8 , if x = -2, what is f(x)? What point is on the graph of f? 38) Given the function f(x) = x-3 A) -

12 12 ; (-2, ) 5 5

B) -

12 12 ; (, -2) 5 5

C)

13

4 4 ; ( , -2) 5 5

D)

4 4 ; (-2, ) 5 5

38)