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Honors Precalculus Semester 1 Review

___ 1. Use the graphs of ( )y f x and ( )y g x to evaluate 1 1 2 .g f

A) –3

B) –1

C) 5

D) 4

E) –2.5

___ 2. Find the inverse function of ( ) 7 – 6f x x

A) + 6( )

7

xg x

C) – 6( )

7

xg x

E) 1( ) + 6

7g x x

B) ( ) –6 + 7g x x D) ( ) –

6

xg x

___ 3. Find .f g

2( ) – 2f x x ( ) –4g x x

A) 2( )( ) + 8 + 14f g x x x C) 2( )( ) –2 – f g x x

E) 2( )( ) –4 – 2f g x x

B) 2( )( ) + 14f g x x D) 2( )( ) –6 – f g x x

___ 4. Find the inverse function of f. 7( ) + 5f x x

A) 1 7( ) + 5f x x C) 1 7( ) + 5f x x E) 1 7( ) – 5f x x

B) 1 7( ) + 5f x x D) 1 7( ) – 5f x x

___ 5. Use a graphing utility to graph the function and determine the increasing and decreasing intervals.

f (x) = x3 + 3x

2 + 2x – 2

A) increasing , 1.58 .42,U

decreasing 1.58, .42

C) increasing , 2.38 1.62,U

decreasing 2.38, 1.62

B) increasing 1.58, .42

decreasing , 1.58 .42,U

D) increasing 2.38, 1.62

decreasing , 2.38 1.62,U

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___ 6. Given

2

9( )

16f x

x

and ( ) 4g x x determine the domain of .f g

A) , –4 4, C) 9 9, ,

4 4

E) ,

B) , –8 –8,0 0, D) , –4 –4,4 4,

___ 7. Use the graph of f to sketch the graph of the function indicated below.

f

A)

C)

E)

B)

D)

___ 8. Find .f g f (x) = x + 3 2

9( )

– 9g x

x

A)

2

9( )( )f g x

x

D) 2

12( )( )

– 9f g x

x

B) 2

9( )( )

+ 6f g x

x x E) 2

2

3 – 18( )( )

– 9

xf g x

x

C) 2

2

3 + 6( )( )

– 9

xf g x

x

___ 9. Determine the vertex of the graph of the quadratic function 2( ) + 4f x x .

A) 0, –4 B) 4,0 C) 4,4 D) 0,4 E) –4,0

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___ 10. Determine the equations of the vertical and horizontal asymptotes of the graph of the function 2

2( )

– 4

xf x

x .

A) horizontal: 1y ; vertical: 2 and –2x x

B) horizontal: –2y ; vertical: 1x

C) horizontal: –1x ; vertical: 2 and –2y y

D) horizontal: 1y ; vertical: 2x

E) horizontal: 2 and –2x x ; vertical: –1y

___ 11. Determine a piecewise-defined function for the graph shown below.

A)

C)

E)

B)

D)

___ 12. Match the graph of the function shown below with the graph of its inverse function

A)

B)

C)

D)

E)

___ 13. Evaluate the function at the specified value of the independent variable and simplify.

( ) 2 2 ( 2.6)q w w q

A) -5.2w – 4 D) -2.6w – 2

B) -3.2 E) -2.6w + 2

C) -7.2

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___ 14. Evaluate the function at the specified value of the independent variable and simplify

3( ) ( 3)

7 5

pg p g y

p

A) 3 9

7 26

y

y

D) 9

16

B) 3 9

7 26

y

y

E) 9

26

C) 3 9

7 26

p

p

___ 15. Restrict the domain of the following function f so that the function is one-to-one and has an

inverse function. 2( ) ( 2) 5f x x

A) [ 5, ) D) ( ,5)

B) [ 2, ) E) [2, )

C) ( , )

___ 16. Find all the rational zeros of the function 4 3 2( ) –2 + 3 + 59 – 75 – 225f x x x x x .

A) 2–3,5, –5,

3x

D) 3 5 3– , – , – , – 5

5 2 2x

B) –2, –15,5x E) 5 3–2, –15, – , –

2 2x

C) 33,5, –5, –

2x

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___ 17. Sketch the graph of the rational function below.

2 1

–1

x xf x

x

A)

C)

E)

B)

D)

___ 18.

Compare the graph of 2

1( ) – + 2 – 4

2q x x

with 2( )q x x .

A)

21

( ) – + 2 – 42

q x x

shifts right 2 units, shifts downward 4 units, and shrinks by a factor of 1

4 .

B)

21

( ) – + 2 – 42

q x x

shifts right 4 units, shifts upward 4 units, and shrinks by a factor of 1

4.

C)

21

( ) – + 2 – 42

q x x

shifts left 2 units, shifts downward 4 units, and shrinks by a factor of 1

4.

D)

21

( ) – + 2 – 42

q x x

shifts right 2 units, shifts upward 4 units, and shrinks by a factor of 1

4.

E)

21

( ) – + 2 – 42

q x x

shifts left 4 units, shifts upward 4 units, and shrinks by a factor of 1

2 .

___ 19. Find all the zeros of the function 5 4 3 2( ) –2 – 9 – 9 – 3 – 7 + 6f x x x x x x .

A) 1, 2, 3

2x

D) 1 3,

2 2x

B) 2– , –1, –2

3x

E) 1, –3, –2,

2x i

C) 1 3, , –2

2 2x

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___ 20. Match the equation with its graph.

A)

C)

E)

B)

D)

___ 21. Using the factors – 5x and – 3x , find the remaining factor(s) of 3 2( ) – 6 – + 30f x x x x and write

the polynomial in fully factored form.

A) ( ) – 5 – 3 + 2f x x x x D) 2

( ) – 5 – 3f x x x

B) 2

( ) – 5 – 3f x x x E) ( ) – 5 – 3 + 6f x x x x

C) ( ) – 5 – 3 – 2f x x x x

___ 22. If 2( ) –4 + + 2f x x x , use synthetic division to evaluate –3f .

A) –3 10f D) –3 –37f

B) –3 35f E) –3 –31f

C) –3 11f

___ 23. Determine the vertex of the graph of the quadratic function

2 5( ) + +

4f x x x .

A)

–1 3,

2 2

B) 5

1,4

C) 1 5

,2 4

D) 1 3

, –4 4

E) –1

,12

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___ 24. Write the quadratic function below in standard form. 2( ) 8 19f x x x

A) 2

( ) 3 1 4f x x D)

2( ) 3 4f x x

B) 2

( ) 3 4 1f x x E)

2( ) 4 1 3f x x

C) 2

( ) 4 3f x x

___ 25. Use long division to divide. 3 + 8 + 2x x

A)

2 – 2 + 4x x B) 2 4x C)

2 + 2 – 4x x D) 2 4x E)

2 24

+ 2x

x

___ 26. Find a third degree polynomial function of the lowest degree that has the zeros below and whose leading

coefficient is one.

8, 1 7, 1 7,

A) 3 2+5 – 5 + 63f x x x x D) 3 2–17 +73 – 57f x x x x

B) 3 2–10 +10 + 48f x x x x E) 3 2+13 + 43 – 57f x x x x

C) 3 2+6 – 62 – 400f x x x x

___ 27. Find the domain of the function below.

ln + 4f x x

A) , –4 B) , –3 C) –4, D) –3, E) 0,

___ 28. Condense the expression below to the logarithm of a single quantity.

5 ln ln + 2 ln – 2x x x

A) 55 2ln – 4x x D) 5

2ln

– 4

x

x

B) 5 55ln + 2 – 2x x x E)

5

2ln

– 4

x

x

C) 5

2ln

– 4

x

x

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___ 29. Identify the operation that will transform the graph of ( ) 4xf x into the graph of

3( ) 4xg x .

A) g(x) is obtained by shifting f(x) 3 units upward (positive).

B) g(x) is obtained by shifting f(x) 3 units downward (negative).

C) g(x) is obtained by shifting f(x) 3 units to the left (negative).

D) g(x) is obtained by shifting f(x) 3 units to the right (positive).

E) g(x) cannot be obtained by any of these tranforms.

Match the graph each graph to its function:

30. 3( ) log 2f x x 32. 3( ) log 2f x x

31. 3( ) logf x x 33. 3( ) log 1f x x

___ 34. Find the exact value of

1.50ln lne e without using a calculator.

A) 0.75 B) 3 C) 1 D) 2 E) 1.5

___ 35. Solve the logarithmic equation below algebraically. Round your result to three decimal

places.

1+5ln 10x

A) 9.608 B) 8.555 C) 6.050 D) 10.598 E) 2.315

___ 36. Determine whether or not

2

7x is a solution to

2 33 81x .

A) yes B) no

___ 37. Identify the operation that will transform the graph of ( ) 4xf x into the graph of

( ) 3 4xg x .

A) g(x) is obtained by reflecting f(x) in the x-axis then shifting upward 3 units.

B) g(x) is obtained by reflecting f(x) in the y-axis then shifting upward 3 units.

C) g(x) is obtained by reflecting f(x) in the x-axis then shifting downward 3 units.

D) g(x) is obtained by reflecting f(x) in the y-axis then shifting downward 3 units.

E) g(x) cannot be obtained by any of these transformations.

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___ 38. Solve the logarithmic equation below algebraically.

2 2log 2 +6 log 3 +5x x

A) –6 B) –1 C) –5 D) –2 E) 1

___ 39. Solve the exponential equation below algebraically. Round your result to three decimal

places.

600

1751 xe

A) –0.163 B) 2.216 C) –1.930 D) 2.336 E) 0.887

___ 40. Simplify the expression 5log 50 .

A) 52 log 2 D)

52log 2

B) 510log 2 E) The expression cannot be simplified.

C) 2

___ 41. Find the domain of the function.

+ 3ln

+1

xf x

x

A) , –1 D) –1,

B) , –3 E) , –3 –1,

C) –3,

___ 42. Approximate the solution to ln5 3.2x . Round to 3 decimal places.

A) 1.896 B) 4.907 C) 4.809 D) –0.446 E) 316.979

___ 43. Solve the logarithmic equation below algebraically.

ln +5 ln +8 ln + 4x x x

A) –5 and –1 B) –2 C) –5 and –2 D) –2 and –1 E) –6 and –2

___ 44. The population P(in thousands) of a city of Nevada can be modeled by P=122ekt, with t=0

corresponding to 1990. In 2000, the population was 169,000. Find the value of k for the

model.

A) 0.7234 D) 0.0326

B) -1.4141 E) 0.0163

C) -0.7240

___ 45. Find the reference angle for the angle 179 . A) 181 B) 89 C) 1 D) –1 E) –89

___ 46. Find the reference angle for the given angle . –188

A) 98 B) –82 C) 18 D) 8 E) –2

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___ 47. Determine the quadrant in which the angle 272.3 lies.

A) Quadrant I B) Quadrant IV C) Quadrant II D) Quadrant III

___ 48. Find the reference angle for the angle –0.6 radians. Round your answer to one decimal place.

A) 2.5 B) –0.6 C) –2.5 D) 0.6 E) –5.7

___ 49. Find the exact value of csc , using the triangle shown in the figure below, if 4 and 3a b .

A) 5

3 B)

5

4 C)

4

3 D)

3

5 E)

4

5

___ 50. A communications company erects a 85-foot tall cellular telephone tower on level ground. Determine the

angle of depression, (in degrees), from the top of the tower to a point 49 feet from the base of the tower.

Round answer to two decimal places.

A) 43.04 B) 51.54 C) 60.04 D) 31.53 E) 56.53

___ 51. Evaluate the tangent of the angle without using a calculator 120

A) – 3 B)

3

3 C)

3–

3 D)

1–

2 E) 0

___ 52. Find two solutions of the equation in the interval [0 ,360 ) . Give your answers in degrees.

A)

D)

B)

E)

C)

a

bc

a

bc

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___ 53. Match the function to the correct graph

( ) sec2

xf x

A)

C)

B)

D)

___ 54. Evaluate the sine of the angle without using a calculator. –150

A)

2–

2 B)

2

2 C)

3–

2 D)

1–

2 E) 0

___ 55.

Evaluate, if possible, the given trigonometric function at the indicated value.

A)

D)

B)

E)

C)

___ 56. Evaluate the trigonometric function using its period as an aid.

35cos –

6

A)

3

2 B)

3–

2 C)

1

2 D)

1

2 E)

2 3

3

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___ 57. In the triangle shown, if B 77 and 12b , find .c Round your answer to two decimals.

A) 12.32 B) 11.69 C) 12.01 D) 53.34 E) 2.70

___ 58. Using the figure below, determine the exact value of the given trigonometric function.

A)

B)

C)

D)

E)

___ 59. Which of the following is equivalent to the expression below?

A)

D)

B)

E)

C)

____60. Find the length of the arc on a circle of radius r intercepted by a central angle .

radius: r = 11 inches central arc:

19

15

A) 19inches

15

D) 209inches

15

B) 209

inches30

E) 209inches

15 C) 2299

inches15

___ 61. A satellite in circular orbit 1125 kilometers above a planet makes one complete revolution

every 120 minutes. Assuming that the planet is a sphere of radius 6400 kilometers, compute

the linear speed of the satellite in kilometers per minute. Round your answer to the nearest

whole number.

A) 22,575 kilometers per minute D) 394 kilometers per minute

B) 3375 kilometers per minute E) 59 kilometers per minute

C) 29 kilometers per minute