Precalculus Exam Packet

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use an inequality to describe the interval of real numbers.1) (-8, 2] 1)

A) -8 x 2 B) -8 < x < 2 C) -8 < x 2 D) x 2

Use interval notation to describe the interval of real numbers.2) x 3 2)

A) [3, ) B) (3, ) C) (- , 3] D) ( , 3)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and itstype.

3) (-5, 1] 3)

4) (-4, -1) 4)

5) (- , 10) 5)

6) [-1, ) 6)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use interval notation to describe the interval of real numbers.7) -6 x < -2 7)

A) [-6, -2) B) (-6 ,-2] C) [-6, -2] D) (-6, -2)

Use an inequality to describe the interval of real numbers.

8) 8)A) 2 < x < 8 B) 2 x < 8 C) 2 x 8 D) 2 < x 8

9) 9)A) x < 3 B) x 3 C) x > 3 D) x 3

1

10) 10)A) x < 5 B) x 5 C) x > 5 D) x 5

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Describe and graph the interval of real numbers.11) (2, 6] 11)

12) (4, ) 12)

13) [2, 7) 13)

14) (- , 5] 14)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Simplify the expression. Assume that the variables in the denominator are nonzero.

15) 3y6

215)

A) y69

B) 9y6

C) 9y12

D) 3y12

Write the number in scientific notation.16) 0.000907 16)

A) 9.07 x 10-5 B) 9.07 x 10-3 C) 9.07 x 104 D) 9.07 x 10-4

Evaluate the expression.17) 6 - -6 17)

A) 12 B) 0 C) 6 D) -12

Find the distance between the points.18) (-3, -1) (-1, 7) 18)

A) 60 B) 6 C) 60 15 D) 2 17

2

19) (4, 6) (-1, -1) 19)A) 35 B) -2 C) 74 D) 24

20) (-4, -3) (6, 2) 20)A) 5 B) 75 C) 5 5 D) 75 3

Evaluate the expression.21) (-2)8 21)

A) 8 B) 16 C) -2 D) -16

22) -4-4

22)

A) -4 B) 1 C) 14

D) -1

Write the number in scientific notation.23) 1,565,540 23)

A) 1.56554 x 106 B) 1.56554 x 10-6 C) 1.56554 x 107 D) 1.56554 x 101

24) 58.7616 24)A) 5.87616 x 10-1 B) 5.87616 x 10-2 C) 5.87616 x 102 D) 5.87616 x 101

25) 0.000457 25)A) 4.57 x 10-5 B) 4.57 x 10-3 C) 4.57 x 10-4 D) 4.57 x 104

26) 0.000066017 26)A) 6.6017 x 105 B) 6.6017 x 10-5 C) 6.6017 x 104 D) 6.6017 x 10-4

Simplify the expression. Assume that the variables in the denominator are nonzero.

27) (2x3)2z5

2z927)

A) x6

z4B) 2x6z4 C) x6

2z4D) 2x6

z4

3

28) 2xy2

-328)

A) x3y68

B) 8x3y6

C) x3y62

D) x3y38

29) x-3y4 -4

y4x-5 -5 29)

A) x8

y4B) y4

x13C) x13

y4D) y4

x8

30) 15a7b5

ab22b2

5a3b730)

A) 6a3

b2B) 1

6a3b2C) 3a3

b2D) 6a3b2

Find the midpoint of the line segment with the given endpoints.

31) -52

, -72

and 52

, -32

31)

A) 0, -52

B) (100, 16) C) -52

, - 1 D) (0, 100)

32) (0, 8) and (3, 3) 32)

A) (3, 11) B) (32

, 112

) C) (-3, 5) D) (- 32

, 52

)

Find the standard form equation for the circle.33) Center (-7, -5), radius 6 33)

A) (x - 7)2 + (y - 5)2 = 36 B) (x - 5)2 + (y - 7)2 = 6C) (x + 5)2 + (y + 7)2 = 6 D) (x + 7)2 + (y + 5)2 = 36

34) Center (-4, 0), radius 9 34)A) (x + 4)2 + y2 = 81 B) (x - 4)2 + y2 = 81C) x2 + (y - 4)2 = 9 D) x2 + (y + 4)2 = 9

4

Find the center and radius of the circle.35) (x - 3)2 + (y - 7)2 = 36 35)

A) (7, 3), r = 6 B) (-7, -3), r = 36 C) (3, 7), r = 6 D) (-3, -7), r = 36

Write the statement using absolute value notation.36) The distance between x and 1 is 4. 36)

A) x - 1 = 4 B) x + 4 = 1 C) x - 4 = 1 D) x + 1 = 4

37) The distance between y and -2 is less than or equal to 6. 37)A) y + 2 < 6 B) y - 2 6 C) y + 2 6 D) y + 2 6

Find the center and radius of the circle.38) x2 + y2 = 7 38)

A) (0, 0), r = 7 B) (1, 1), r = 7 C) (1,1), r = 7 D) (0, 0), r = 7

Find which values of x are solutions.39) 3x2 - 14x = 5

(a) x = 5 (b) x = 0 (c) x = -13

39)

A) (a) B) (a) and (b) C) (b) D) (a) and (c)

40) 3x2 - 11x = 4

(a) x = 4 (b) x = 0 (c) x = -13

40)

A) (a) and (b) B) (a) and (c) C) (a) D) (b)

41) x2

+16

=x5

(a) x = 0 (b) x = -59

(c) x = 1

41)

A) (a) B) (a) and (b) C) (b) and (c) D) (b)

42) 9 - x2 + 3 = 6(a) x = 3 (b) x = -3 (c) x = 0

42)

A) (a) and (b) B) (c) C) (b) D) (a) and (c)

5

Solve the equation.

43) 14

(12x - 20) =15

(25x - 15) 43)

A) x = -1 B) x = -8 C) x =18

D) x = 1

44) x + 56

=x + 6

744)

A) x =1

42B) x =

1142

C) x =1113

D) x = 1

45) 9x + 12

+2x + 4

5= 4 45)

A) x =4349

B) x =2749

C) x =5349

D) x = -949

Solve the inequality.

46) 10 5x + 23

-5 46)

A) x -175

B) -175

x 285

C) -175

< x <285

D) x 285

47) 1 >4z +1

7> -1 47)

A) 32

< z < 2 B) - 2 < z < -32

C) - 2 < z <32

D) -32

< z < 2

6

48) 4y - 23

+5y + 1

5 y + 1 48)

A) y 1110

B) y 12

C) y -110

D) y 225

49) 14

(x + 3) - 4x 3(1 + x) 49)

A) x 19

B) x 19

C) x -13

D) x -13

Find the value of x or y so that the line through the pair of points has the given slope.50) (-1, 2) and (4, y); m = -2 50)

A) 9 B) -9 C) 11 D) -8

Find a general form equation for the line through the pair of points.51) (-1, 3) and (5, 1) 51)

A) 2x - 6y - 16 = 0 B) 2x + 6y - 16 = 0C) -2x - 6y - 16 = 0 D) 2x + 6y + 16 = 0

Find a slope-intercept form equation for the line.

52) Through (4, 5), with slope -37

52)

A) y = -37

x +477

B) y =37

x +127

C) y = -37

x +127

D) y =37

x -477

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.53) Through (1, 13), parallel to -5x + 9y = 67 53)

A) y =95

x -135

B) y = -59

x -1129

C) y = -19

x +679

D) y =59

x +1129

7

Solve the equation by factoring.54) x2 - x = 56 54)

A) x = 1 or x = 56 B) x = 7 or x = 8 C) x = -7 or x = 8 D) x = -7 or x = -8

Solve the equation by extracting the square roots.55) (r + 5)2 = 11 55)

A) r = 11 or r = 11 B) r = 5 + 11 or r = 5 - 11C) r = -5 + 11 or r = -5 - 11 D) r = 6 or r = - 6

Solve by completing the square.56) x2 + 12x + 11 = 0 56)

A) 11, - 11 B) 22, -11 C) 1, 11 D) -1, -11

57) 4x2 + 35 = -24x 57)

A) -52

, -72

B) -74

, 212

C) 52

, 72

D) -54

, -74

Solve the equation by factoring.58) 16x2 + 32x + 15 = 0 58)

A) x = -54

or x = -34

B) x =54

or x =34

C) x =45

or x =43

D) x = -45

or x = -34

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.59) Through (-3, 9), perpendicular to -5x + 6y = -39 59)

A) y = -12

x +132

B) y =65

x +275

C) y = -65

x +275

D) y = -56

x -56

8

Solve the equation using the quadratic formula.60) 5x2 + 12x + 6 = 0 60)

A) x =-6 + 6

10 or x =

-6 - 610

B) x =-6 + 6

5 or x =

-6 - 6 5

C) x =-12 + 6

5 or x =

-12 - 65

D) x =-6 + 66

5 or x =

-6 - 665

Solve the equation graphically by finding x-intercepts.61) 2x2 + 11x + 4 = 0 61)

A) x = -2.36 or x = 2.36 B) x = 0 or x = 2.36C) x =-0.39 or x = 1.97 D) x = -5.11 or x = -0.39

Write the sum or difference in the standard form a + bi.62) (8 - 9i) + (5 + 6i) 62)

A) 13 + 3i B) 13 - 3i C) -13 + 3i D) 3 + 15i

63) (7 + 9i) - (-5 + i) 63)A) -12 - 8i B) 12 - 8i C) 12 + 8i D) 2 + 10i

Write the product in standard form.64) (7 - 3i)(7 + 6i) 64)

A) 31 - 63i B) 67 - 21i C) -18i2 + 21i + 49 D) 67 + 21i

Perform the indicated operation. Write the result in standard form.65) (-2 + 3i)3 65)

A) 46 + 107i B) 46 + 36i + i3

C) 46 + 9i D) 8 - 54i2 + 36i + i3

9

Write the expression in standard form.

66) 9+ i-2 - 6i

66)

A) -35

+1310

i B) -35

-1310

i C) 1310

i D) -35

Solve the equation.67) x2 + x + 4 = 0 67)

A) -12

± 152

i B) 12

± 152

i C) 12

± 152

D) -12

± 152

Solve the inequality algebraically. Write the solution in interval notation.68) 4x - 5 6 68)

A) (- , -114

] [6, ) B) (- , -14

] [ 114

, )

C) [- 14

, 114

] D) [114

, )

Solve the inequality. Use algebra to solve the corresponding equation.69) x2 - 4x - 21 < 0 69)

A) (- , -3) (7, ) B) (7, ) C) (-3, 7) D) (- , -3)

70) x2 - 11x + 30 0 70)A) [5, 6] B) [6, ) C) (- , 5] D) (- , 5] [6, )

10

Solve the inequality graphically.71) x2 + 2x 3 71)

A) [1, ) B) [-3, 1] C) (- , -3] D) (- , -3] [1, )

72) x2 + 8 -4x 72)

A) No solution B) (- , ) C) (8, ) D) (- , -4)

Determine whether the formula determines y as a function of x.73) y = 5x2 - 9x - 2 73)

A) Yes B) No

74) x = y2 + 5 74)A) No B) Yes

11

75) y2 = (x - 7)(x + 7) 75)A) Yes B) No

Determine whether the graph is the graph of a function.76) 76)

A) No B) Yes

77) 77)

A) No B) Yes

78) 78)

A) Yes B) No

12

Find the domain of the given function.

79) f x =4x2

79)

A) (- ,0) (0, ) B) [0, )C) All real numbers D) (- ,3] [3, )

80) f(x) = 9 - x 80)A) ( 9, ) B) All real numbersC) (- , 9] D) (- ,9) (9, )

81) f(x) =x

x - 981)

A) (- ,-9) (-9, ) B) (- ,9) (9, )C) All real numbers D) (0, )

82) f(x) =(x + 3)(x - 3)

x2 + 982)

A) (- ,3) (-3,3) (3, ) B) All real numbersC) (9, ) D) (- ,-9) (-9,9) (9, )

83) f(x) =9 - x2x - 1

83)

A) (- , -3) (3, ) B) [-3, 1) (1, 3] C) [-9, 1) (1, 9] D) [-3, 3]

Find the range of the function.84) f(x) = x2 + 3 84)

A) (-3, ) B) (- , ) C) (- , 3 ] D) [3, )

85) f(x) = 7 + x 85)A) (0, ) B) [0, ) C) (- , ) D) [-7, )

13

86) f(x) = 7 - x2 86)A) (- , 7] B) (- , ) C) [- 7, 7 ] D) [7, )

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it isremovable or non-removable.

87) f(x) =1x

87)

A)

No

B)

NoC)

Yes; non-removable

D)

Yes; removable

14

88) h(x) =x

x - 188)

A)

No

B)

Yes; non-removableC)

No

D)

Yes; non-removable

15

Solve the problem.89) Use the graph of f to estimate the local maximum and local minimum. 89)

A) Local maximum: -1; local minimum: 2B) No local maximum; no local minimumC) Local maximum: ; local minimum: -

D) Local maximum: approx. 1.17; local minimum: approx. -3.33

90) Use the graph of f to estimate the local maximum and local minimum. 90)

A) No local maximum; local minimum: -4B) Local maximum: 0; local minimum: -4C) Local maximum: ; local minima: -2 and 2D) Local maximum: 0; local minima: -2 and 2

16

Determine the intervals on which the function is increasing, decreasing, and constant.91) 91)

A) Increasing on (-3, -1); Decreasing on (-5, -2) and (2, 4); Constant on (-1, 2)B) Increasing on (-3, 1); Decreasing on (-5, -3) and (0, 5); Constant on (1, 2)C) Increasing on (-3, 0); Decreasing on (-5, -3) and (2, 5); Constant on (0, 2)D) Increasing on (-5, -3) and (2, 5); Decreasing on (-3, 0); Constant on (0, 2)

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain.92) y = 3 - x2 92)

A) Bounded domain B) UnboundedC) Bounded above D) Bounded below

93) y = 2 - x2 93)A) Bounded B) Bounded aboveC) Unbounded D) Bounded below

Determine algebraically whether the function is even, odd, or neither even nor odd.94) f(x) = 3x2 - 1 94)

A) Even B) Neither C) Odd

95) f(x) = -9x3 + 8x 95)A) Neither B) Odd C) Even

96) f(x) = -9x4 + 5x + 3 96)A) Odd B) Neither C) Even

17

Find the asymptote(s) of the given function.

97) f(x) =x - 1x2 + 2

vertical asymptotes(s) 97)

A) None B) x = 1, x = -1 C) x = -2 D) x = 2

98) h(x) =(x - 3)(x + 1)

x2 - 1 vertical asymptotes(s) 98)

A) None B) x = 1, x = -1 C) x = -3, x = 1 D) x = 3, x = -1

99) f(x) =9x2 + 99x2 - 9

horizontal asymptotes(s) 99)

A) y = 1 B) y = -9 C) None D) y = 9

100) g(x) =x2 + 5x - 2

x - 2 horizontal asymptotes(s) 100)

A) None B) y = 2 C) y = -5 D) y = 8

Perform the requested operation or operations. Find the domain of each.101) f(x) = 7x + 7, g(x) = 6x2

Find (fg)(x).101)

A) 42x2 + 42x; domain: (- , ) B) 42x + 42; domain: (- , )C) 42x3+ 42x2; domain: (- , ) D) 6x2 + 7x + 7; domain: (- , )

102) f(x) = 4x + 7, g(x) = 3x2Find (f + g)(x).

102)

A) 12x3 + 21x; domain: (- , ) B) 4x + 7 + 3x2; domain: (- , )

C) 4x + 73x2

; domain: (- , ) D) 4x + 7 - 3x2; domain: (- , )

18

103) f(x) = 3x + 2; g(x) = 3x - 5Find f/g.

103)

A) (f/g)(x) =3x + 23x - 5

; domain {x|x -23

} B) (f/g)(x) =3x + 23x - 5

; domain {x|x 53

}

C) (f/g)(x) =3x - 53x + 2

; domain {x|x -23

} D) (f/g)(x) =3x - 53x + 2

; domain {x|x 53

}

Perform the requested operation or operations.104) f(x) = x + 6; g(x) = 8x - 10

Find f(g(x)).104)

A) f(g(x)) = 2 2x - 1 B) f(g(x)) = 8 x - 4C) f(g(x)) = 2 2x + 1 D) f(g(x)) = 8 x + 6 - 10

105) f(x) =x - 5

8; g(x) = 8x + 5, find g(f(x)). 105)

A) g(f(x)) = 8x + 35 B) g(f(x)) = x

C) g(f(x)) = x + 10 D) g(f(x)) = x -58

106) f(x) = 4x2 + 5x + 3; g(x) = 5x - 7, find g(f(x)). 106)A) g(f(x)) = 4x2 + 25x + 8 B) g(f(x)) = 4x2 + 5x - 4C) g(f(x)) = 20x2 + 25x + 22 D) g(f(x)) = 20x2 + 25x + 8

Find f(x) and g(x) so that the function can be described as y = f(g(x)).107) y = 10x + 6 107)

A) f(x) = -x , g(x) = 10x - 6 B) f(x) = x, g(x) = 10x + 6C) f(x) = x , g(x) = 10x + 6 D) f(x) = - x , g(x) = 10x + 6

19

108) y =4x2

+ 9 108)

A) f(x) =4x2

, g(x) = 9 B) f(x) = x + 9, g(x) =4x2

C) f(x) = x, g(x) =4x

+ 9 D) f(x) =1x

, g(x) =4x

+ 9

Find two functions defined implicitly by the given relation.109) x + y2 = 9 109)

A) y = 9- x or y = 9 + x B) y = 9 - x or y = - 9 - xC) y = 9 - x or y = 9 + x D) y = 9 - x or y = -9 + x

Find the (x,y) pair for the value of the parameter.110) x = t3 - 9t and y = t - 1 for t = 1 110)

A) (0, 10) B) (-8, 0) C) (10, 0) D) (0, -8)

Find a direct relationship between x and y.111) x = t - 5 and y = t2 + t 111)

A) y = x2 + x + 30 B) y = x2 - 9x + 20C) y = x2 + x + 20 D) y = x2 + 11x + 30

112) x = t - 5 and y = t2 - 6t 112)A) y = x2 + 11x + 30 B) y = x2 + x + 20C) y = x2 - 16x + 55 D) y = x2 + 4x - 5

20

Find the inverse of the function.113) f(x) = 3x - 2 113)

A) f-1(x) =x - 2

3B) f-1(x) =

x3

+ 2

C) f-1(x) =x + 2

3D) Not a one-to-one function

114) f(x) = x3 + 4 114)

A) Not a one-to-one function B) f-1(x) =3

x - 4

C) f-1(x) =3

x - 4 D) f-1(x) =3

x + 4

115) f(x) =8

x + 8115)

A) f-1(x) =-8x + 8

xB) f-1(x) =

8 + 8xx

C) f-1(x) =x

8 + 8xD) Not invertible

Determine if the function is one-to-one.116) 116)

A) No B) Yes

21

117) 117)

A) Yes B) No

118) 118)

A) No B) Yes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

119) f(x) = 9x + 3 and g(x) =x - 3

9119)

120) f(x) = x3 + 4 and g(x) =3

x - 4 120)

121) f(x) = x2 - 3 and g(x) = 3 + x 121)

22

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Describe how to transform the graph of f into the graph of g.122) f(x) = x and g(x) = 7 x 122)

A) Horizontally shrink the graph of f by a factor of 17

.

B) Vertically stretch the graph of f by a factor of 7.C) Horizontally stretch the graph of f by a factor of 7.

D) Vertically shrink the graph of f by a factor of 17

.

123) f(x) = x and g(x) = - x + 3 123)A) Shift the graph of f right 3 units and then reflect across the x-axis.B) Shift the graph of f up 3 units and then reflect across the y-axis.C) Shift the graph of f left 3 units and then reflect across the y-axis.D) Shift the graph of f left 3 units and then reflect across the x-axis.

The graph is that of a function y = f(x) that can be obtained by transforming the graph of y = x . Write a formula forthe function f.

124) 124)

A) f(x) = x - 3 B) f(x) = x + 3 C) f(x) = x + 3 D) f(x) = x - 3

125) 125)

A) f(x) = - x + 3 B) f(x) = -x + 3 C) f(x) = -x + 3 D) f(x) = - x + 3

23

Give the equation of the function g whose graph is described.126) The graph of f(x) = x is shifted 3 units to the left. Then the graph is shifted 6 units upward. 126)

A) g(x) = 6 x + 3 B) g(x) = x + 3 + 6C) g(x) = x - 3 + 6 D) g(x) = x + 6 + 3

127) The graph of f(x) = x is vertically stretched by a factor of 4.8. This graph is then reflected acrossthe x-axis. Finally, the graph is shifted 0.3 units downward.

127)

A) g(x) = 4.8 x - 0.3 B) g(x) = 4.8 -x - 0.3C) g(x) = 4.8 x - 0.3 D) g(x) = -4.8 x - 0.3

128) The graph of f(x) = 6 x - 1 + 5 is reflected across the x-axis . 128)A) g(x) = 6 -x - 1 - 5 B) g(x) = - 6 x - 1 + 5C) g(x) = 6 -x - 1 + 5 D) g(x) = - 6 x - 1 - 5

129) The graph of f(x) = x2 is vertically stretched by a factor of 8, and the resulting graph is reflectedacross the x-axis.

129)

A) g(x) = -8x2 B) g(x) = 8x2

C) g(x) = 8(x - 8)x2 D) g(x) = (x - 8)2

130) The graph of f(x) = x3 is shifted 5.7 units to the right and then vertically shrunk by a factor of 0.7. 130)A) g(x) = 5.7(x - 0.7)3 B) g(x) = 0.7(x + 5.7)3

C) g(x) = 0.7(x - 5.7)3 D) g(x) = 0.7x3 + 5.7

24

Match the equation to the correct graph.131) f(x) = 2 - 3(x - 5)2 131)

A) B)

C) D)

132) y = 2(x + 3)2 - 3 132)

A) B)

C) D)

25

133) f(x) = 3 - 4(x - 3)2 133)A) B)

C) D)

Find the vertex of the graph of the function.134) f(x) = (x - 8)2 - 1 134)

A) (-1, 0) B) (0, 8) C) (-1, 8) D) (8, -1)

Find the axis of the graph of the function.135) f(x) = (x + 1)2 + 7 135)

A) y = -1 B) x = 0 C) x = 1 D) x = -1

136) f(x) = 4x2 - 24x + 37 136)A) x = 3 B) x = 0 C) x = 1 D) x = -2

Write the quadratic function in vertex form.137) y = x2 + 4x + 7 137)

A) y = (x - 2)2 - 3 B) y = (x + 2)2 + 3 C) y = (x + 2)2 - 3 D) y = (x - 2)2 + 3

26

Write an equation for the quadratic function whose graph contains the given vertex and point.138) Vertex (5, 4), point (6, 5) 138)

A) P(x) = 6x2 - 10x + 29 B) P(x) = x2 - 5x + 4C) P(x) = x2 - 10x + 29 D) P(x) = - x2 - 10x + 4

139)

(Write your answer in vertex form.)

139)

A) P(x) = (x - 3)2 - 2 B) P(x) = (x + 2)2 - 3C) P(x) = (x - 2)2 - 3 D) P(x) = (x + 3)2 - 2

Solve the problem.140) Bill Monotone sells used CDs for $9.00 each. Each used CD costs him $3.00. His overhead is $6300.

Express the cost C as a function of x where x is the number of CDs sold.140)

A) C(x) = 9.00x + 6300 B) C(x) = 6300x + 9.00C) C(x) = 6300x + 3.00 D) C(x) = 3.00x + 6300

27

141) A projectile is thrown upward so that its distance above the ground after t seconds ish = -16t2 + 672t. After how many seconds does it reach its maximum height?

141)

A) 21 s B) 10 s C) 42 s D) 31.5 s

Determine if the function is a power function. If it is, then state the power and constant of variation.

142) f(x) =17

x5 142)

A) Power is 5; constant of variation is 17

B) Power is 5; constant of variation is 1

C) Not a power function D) Power is 17

; constant of variation is 5

143) f(x) = 4 · 5x 143)A) Not a power function B) Power is x; constant of variation is 20C) Power is 5; constant of variation is 4 D) Power is x; constant of variation is 4

144) S = 4 r2 144)A) Power is 2; constant of variation is 4 B) Not a power functionC) Power is 2; constant of variation is 4 D) Power is 4 ; constant of variation is 2

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree andleading coefficient.

145) f(x) = -5 · x3 145)A) Degree is -5; leading coefficient is 3 B) Degree is 3; leading coefficient is -5C) Not a monomial function D) Degree is 3; leading coefficient is 5

146) f(x) = -6 · 6x 146)A) Degree is 6; leading coefficient is -6 B) Degree is x; leading coefficient is 6C) Not a monomial function D) Degree is x; leading coefficient is -6

147) I(d) =k

d2147)

A) Degree is 2; leading coefficient is k B) Degree is -2; leading coefficient is kC) Not a monomial function D) Degree is 2; leading coefficient is I

28

Write the statement as a power function equation. Use k as the constant of variation.148) The height h of a cone with a fixed volume varies inversely as the square of its radius r. 148)

A) h =r2k

B) r2 = kh C) h =kr2

D) h = kr2

149) The surface area of a sphere S varies directly as the square of its radius r. 149)

A) S =r2k

B) S = k2r C) S = kr2 D) S =kr2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

State the power and constant of variation for the function, and then analyze it.150) f(x) = 4x3 150)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the power function is even, odd, or neither.151) f(x) = 6x1/7 151)

A) Even B) Odd C) Neither

152) f(x) = -9x2/5 152)A) Neither B) Odd C) Even

29

Solve the problem.153) The table shows the population of a certain city in various different years. Use regression to find

values for a and b so that f(x) = axb models this data, where x represents the number of yearssince 1980 and f(x) is the population of the city in hundreds of thousands. Round your answers to 4decimal places.

Year 1981 1985 1989 1993 1997Population (hundreds of thousands) 3.2 4.1 5.7 9.6 14.1

153)

A) a 1.7025, b 0.5375 B) a 1.8506, b 0.5121C) a 2.6352, b 0.4756 D) a 2.1375, b 0.4432

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the givenpolynomial function. Then sketch the transformed graph.

154) g(x) = -(x + 6)3 154)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the given graph with its polynomial function.155) 155)

A) f(x) = x3 + x2 + x + 5 B) f(x) = -x3 + 4x2 + x - 5C) f(x) = x5 + 4x3 - x2 + 3x - 5 D) f(x) = x3 + 4x2 - x - 5

30

Graph the function in a viewing window that shows all of its extrema and x-intercepts.156) f(x) = 2x(x + 2)(x + 1) 156)

A) B)

C) D)

Describe the end behavior of the polynomial function by finding limx

f x and limx

f x .

157) f(x) = 4x4 + 3x2 + 9 157)A) , B) , C) , D) ,

158) f(x) = -4x4 + 2x2 - 3 158)A) , B) , C) , D) ,

Find the zeros of the function.159) f(x) = x2 + 5x + 4 159)

A) 1 and -4 B) -1 and 4 C) 1 and 4 D) -1 and -4

31

160) f(x) = 9x2 + 6x - 8 160)

A) 23

and -43

B) -2 and 4 C) -23

and 43

D) 2 and -4

Find the zeros of the polynomial function and state the multiplicity of each.161) f(x) = 3(x + 8)2(x - 8)3 161)

A) -8, multiplicity 3; 8, multiplicity 2B) 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3C) -8, multiplicity 2; 8, multiplicity 3D) 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

Graph the function.162) P(x) = -2x(x + 1)(x - 2) 162)

A) B)

C) D)

32

Find a cubic function with the given zeros.163) -7, 6, -5 163)

A) f(x) = x3 + 6x2 + 37x - 210 B) f(x) = x3 + 6x2 - 37x + 210C) f(x) = x3 - 6x2 - 37x - 210 D) f(x) = x3 + 6x2 - 37x - 210

Divide f(x) by d(x), and write a summary statement in the form indicated.164) f(x) = x3 + 5; d(x) = x + 4 (Write answer in polynomial form) 164)

A) f(x) = (x + 4)(x2 - 4x + 16) - 59 B) f(x) = (x + 4)(x2 + 4x + 16) - 64C) f(x) = (x + 4)(x2 - 4x + 16) - 64 D) f(x) = (x + 4)(x2 + 4x + 16) - 59

165) f(x) = x3 + 7x2 + 10x - 1; d(x) = x + 6 (Write answer in polynomial form) 165)A) f(x) = (x + 6)(x2 - x + 4) - 25 B) f(x) = (x + 6)(x2 + x + 4) - 25C) f(x) = (x + 6)(x2 + x + 4) + 25 D) f(x) = (x + 6)(x2 + x - 4) + 25

166) f(x) = x2 - 2x + 6; d(x) = x - 7 (Write answer in fraction form) 166)

A) f(x)(x - 7)

= (x - 7) +35

(x - 7)B) f(x)

(x - 7)= (x + 5) +

35(x - 7)

C) f(x)(x - 7)

= (x + 5) +41

(x - 7)D) f(x)

(x - 7)= (x - 7) +

41(x - 7)

33

Divide using synthetic division, and write a summary statement in fraction form.

167) 2x3 + 3x2 + 4x - 10x + 1

167)

A) 2x2 + x + 3 +13

x + 1B) 2x2 + 5x + 9 +

-1x + 1

C) 2x2 + x + 3 +-13x + 1

D) 2x2 + 5x + 9 +1

x + 1

Find the remainder when f(x) is divided by (x - k)168) f(x) = 2x3 + 6x2 + 3x + 22; k= -3 168)

A) 31 B) 13 C) -255 D) -121

Use the Rational Zeros Theorem to write a list of all potential rational zeros169) f(x) = 2x3 + 6x2 + 13x - 8 169)

A) ±1, ±2, ±4, ±8 B) ±1, ± 12

, ±2, ±4, ±8

C) ±1, ± 12

, ± 14

, ± 18

, ±2 D) ±1, ±2, ±4

Find all rational zeros.170) f(x) = 4x3 - 16x2 - x + 4 170)

A) 12

, -12

, 4 B) 2, -2, 4 C) 12

, -12

, -4 D) 1, -1, 4

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zerosof the function f.

171) k = 2; f(x) = 7x3 + 6x2 + 5x + 2; Upper bound? 171)A) Yes B) No

172) k = -2; f(x) = x3 + 5x2 + 2x + 4; Lower bound? 172)A) Yes B) No

34

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational orirrational.

173) f(x) = x3 + 4x2 - 3x - 12 173)A) -4 (rational), 3 (rational), and -3 (rational)B) 4 (rational), 3 (irrational), and - 3 (irrational)C) -4 (rational), 2 3 (irrational), and -2 3 (irrational)D) -4 (rational), 3 (irrational), and - 3 (irrational)

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write thepolynomial in standard form.

174) 3 and 2 - i 174)A) f x = x3 - 7x2 + 17x + 15 B) f x = x3 - 7x2 + 17x - 12C) f x = x3 + 7x2 + 17x - 15 D) f x = x3 - 7x2 + 17x - 15

Write a linear factorization of the function.175) f(x) = x3 + 2x2 + 2x - 5 175)

A) f(x) = (x - 1)(2x + 3 + 11i)(2x + 3 - 11i) B) f(x) = (x + 1)(2x + 3 + 7i)(2x + 3 - 7i)C) f(x) = (x + 1)(2x + 3 + 11i)(2x + 3 - 11i) D) f(x) = (x - 1)(x + 3 + 11i)(x + 3 - 11i)

35

Using the given zero, find all other zeros of f(x).176) i is a zero of f(x) = x4 - 4x3 + 2x2 - 4x + 1 176)

A) -i, -2 + 3, -2 - 3 B) -i, 2 + 3, 2 - 3C) -i, 1 + 3, 1 - 3 D) -i, 2 + 2 3, 2 - 2 3

State the domain of the rational function.

177) f(x) =7

14 - x177)

A) (- , - 7) (- 7, 7) (7, ) B) (- , 7) (7, )C) (- , 14) (14, ) D) (- , - 14) (- 14, 14) (14, )

178) f(x) =x - 9x2 + 5

178)

A) (- , 5) (5, ) B) (- , - 3) (- 3, 3) (3, )C) (- , ) D) (- , -5) (-5, )

Use limits to describe the behavior of the rational function near the indicated asymptote.

179) f(x) = -8

x + 2Describe the behavior of the function near its vertical asymptote.

179)

A) limx -2-

f(x) = , limx -2+

f(x) = B) limx 2-

f(x) = , limx 2+

f(x) = -

C) limx -2-

f(x) = 0, limx -2+

f(x) = 0 D) limx -2-

f(x) = , limx -2+

f(x) = -

180) f(x) =x + 1

x2 - 2xDescribe the behavior of the function near its horizontal asymptote (the end behavior).

180)

A) limx -

f(x) = 0, limx

f(x) = 0 B) limx -

f(x) = - , limx

f(x) =

C) limx -

f(x) = -1, limx

f(x) = 1 D) limx 0-

f(x) = , limx 0+

f(x) =

36

Evaluate the limit based on the graph of f shown.181)

limx -4-

f x

181)

A) B) 4 C) D) 0

182)

limx 1+

f x

182)

A) B) 1 C) D) 0

37

183)

limx -1-

f x

183)

A) B) 1 C) 0 D)

184)

limx -3+

f x

184)

A) B) -3 C) 0 D)

38

185)

limx -4+

f x

185)

A) B) 14

C) D) 0

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

186)

limx

f x

186)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

List the x- and y-intercepts, and graph the function.

39

187) f(x) =x - 1

x2 - 5x - 6187)

A) x-intercept: (-1, 0) , y-intercept: 0, -112

;

B) x-intercept: (-1, 0) , y-intercept: 0, 112

;

C) x-intercept: (1, 0) , y-intercept: 0, 16

;

40

D) x-intercept: (1, 0) , y-intercept: 0, -16

;

188) f(x) =x2 - 16x + 2

188)

A) x-intercepts: (-4, 0) and (4, 0) , y-intercept: 0, 8

B) x-intercept: (0, 0) , y-intercept: (0, 0) ;

41

C) x-intercepts: (-4, 0) and (4, 0) , y-intercept: 0, - 8

D) x-intercept: (0, 0) , y-intercept: (0, 0) ;

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Graph the rational function and analyze it in the following way: find the intercepts, asymptotes, use limits to describethe behavior at the vertical asymptotes and the end behavior. Find the domain and range. Determine where thefunction is continuous and where it is increasing and decreasing. Find any local extrema.

189) f(x) =2

x2 - 2x - 3189)

42

190) f(x) =x2 + x - 2x2 - 3x - 4

190)

191) f(x) =x2 - x - 6

x - 2191)

43