Chapter 1 Test Review s1
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Chapter 1 Test Review
Multiple Choice Identify the choice that best completes the statement or answers the question.
____ 1. Find the zeros of the function algebraically.
a. b. c. d. e.
____ 2. Find the zeros of the function algebraically.
a.
b.
c.
d.
e.
____ 3. Find the average rate of change of the function from to .
a. The average rate of change from to is . b. The average rate of change from to is . c. The average rate of change from to is 6. d. The average rate of change from to is . e. The average rate of change from to is .
____ 4. Select the graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.
a. d. y y 8 8
6 6
4 4
2 2
–8 –6 –4 –2 2 4 6 8 x –8 –6 –4 –2 2 4 6 8 x –2 –2
–4 –4
–6 –6
–8 –8
O E dd ven b. e. y y 8 8
6 6
4 4
2 2
–8 –6 –4 –2 2 4 6 8 x –8 –6 –4 –2 2 4 6 8 x –2 –2
–4 –4
–6 –6
–8 –8
N O either dd c. y 8
6
4
2
–8 –6 –4 –2 2 4 6 8 x –2
–4
–6
–8
Neither
____ 5. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.
a.
b.
c. d.
e.
____ 6. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.
a.
b.
c. d.
e.
____ 7. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.
a.
b.
c.
d.
e.
____ 8. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even and odd.
a. b.
c.
d.
e.
____ 9. Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
a.
b.
c.
d.
e.
____ 10. Select the correct graph of the given function.
a. d. y y 10 10
8 8
6 6
4 4
2 2
–20 –16 –12 –8 –4 4 8 12 16 20 x –20 –16 –12 –8 –4 4 8 12 16 20 x –2 –2
–4 –4
–6 –6
–8 –8
–10 –10
b. e. y y 3 10
8 2 6
4 1 2
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –2 –1 –4
–6 –2 –8
–3 –10
c. y
9
6
3
–20 –16 –12 –8 –4 4 8 12 16 20 x –3
–6
–9
____ 11. Select the correct graph of the given function. a. d. y y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5 b. e. y y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5 c. y 5
4
3
2
1
–5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
____ 12. Select the correct graph of the given function.
a. d. y y 7 7 6 6 5 5 4 4 3 3 2 2 1 1
–5 –4 –3 –2 –1–1 1 2 3 4 5 x –5 –4 –3 –2 –1–1 1 2 3 4 5 x –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7
b. e. y y 7 7 6 6 5 5 4 4 3 3 2 2 1 1
–5 –4 –3 –2 –1–1 1 2 3 4 5 x –5 –4 –3 –2 –1–1 1 2 3 4 5 x –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7
c. y 7 6 5 4 3 2 1
–5 –4 –3 –2 –1–1 1 2 3 4 5 x –2 –3 –4 –5 –6 –7
____ 13. Select the correct graph of the given function. a. y d. y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5
b. y e. y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5
c. y 5
4
3
2
1
–5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
____ 14. Select the correct graph of the given function. a. d. y y 5 5
4 4
3 3
2 2
1 1
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5 b. e. y y 5 5
4 4
3 3
2 2
1 1
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5 c. y 5
4
3
2
1
–10 –8 –6 –4 –2 2 4 6 8 10 x –1
–2
–3
–4
–5 ____ 15. Evaluate the function for .
a. b. c. d. e.
____ 16. Select the graph of the function:
a. d. y y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5
b. e. y y 5 5
4 4
3 3
2 2
1 1
–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –1
–2 –2
–3 –3
–4 –4
–5 –5
c. y 5
4
3
2
1
–5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
____ 17. Which graph represents the function?
g(x) = a.
b. c.
d.
e.
____ 18. Use the graph of to write an equation for the function whose graph is shown.
y
16
12
8
4
–8 –4 4 8 x a.
b.
c.
d.
e.
____ 19. Identify the parent function and the transformation shown in the graph. Write an equation for the function shown in the graph.
y
8
4
4 8 12 16 x
–4
–8
a. Horizontal shift of b. Vertical shift of c. Vertical shift of d. Horizontal shift of e. Vertical shift of
____ 20. Identify the parent function and the transformation shown in the graph. Write an equation for the function shown in the graph. y 20
16
12
8
4
–8 –4 4 8 x
a. Reflection in the -axis of b. Horizontal shift of -axis of c. Reflection in the -axis of d. Reflection in the -axis of e. Reflection in the -axis of
____ 21. Indentify the parent function . The parent function is related to .
a.
b.
c.
d.
e.
____ 22. is related to the parent function, select the graph of . a. d. y y
8 8
4 4
–8 –4 4 8 x –8 –4 4 8 x
–4 –4
–8 –8
b. e. y y
8 8
4 4
–8 –4 4 8 x –8 –4 4 8 x
–4 –4
–8 –8
c. y
8
4
–8 –4 4 8 x
–4
–8 ____ 23. is related to the parent function. Use function notation to write in terms of .
a.
b.
c.
d.
e.
____ 24. is related to the parent function. Select the graph of .
a. d. y 20 y 16 20
12 16
8 12
4 8
4 –20 –16 –12 –8 –4 4 8 12 16 20 x –4 –20 –16 –12 –8 –4 4 8 12 16 20 x –8 –4
–12 –8
–16 –12
–20 –16
–20
b. e. y y 20 20
16 16
12 12
8 8
4 4
–20 –16 –12 –8 –4 4 8 12 16 20 x –20 –16 –12 –8 –4 4 8 12 16 20 x –4 –4
–8 –8
–12 –12
–16 –16
–20 –20
c. y 20
16
12
8
4
–20 –16 –12 –8 –4 4 8 12 16 20 x –4
–8
–12
–16
–20
____ 25. Write an equation for the function that is described by the given characteristic.
The shape of , but shifted units to the left and reflected in both the -axis and the -axis.
a.
b.
c.
d.
e. ____ 26. Use the graph of to write an equation for each function whose graph is shown.
y
12
8
4 (–2, 3)
–8 –4 4 8 x
–4
a.
b.
c.
d.
e.
____ 27. Use the graph of
to write an equation for the function whose graph is shown. a.
b.
c.
d.
e.
____ 28. Write an equation for the function that is described by the following characteristics:
the shape of , but moved eight units down, two units to the left, and then reflected in the x-axis a.
b.
c.
d.
e.
____ 29. Find .
,
a. b. 12 c. d. e.
____ 30. Find .
,
a. b.
c.
d.
e.
____ 31. Find .
,
a.
b.
c.
d.
e.
____ 32. Evaluate the indicated function for and .
a. 17 b. 23 c. –23 d. 27 e. –2
____ 33. Evaluate the indicated function for and .
a.
b. c.
d.
e.
____ 34. Find .
,
a.
b.
c.
d.
e.
____ 35. Find fog and the domain of composite function.
,
a.
Domain of fog: all real numbers x except b.
Domain of fog: all real numbers x except c.
Domain of fog: all real numbers x except d.
Domain of fog: all real numbers x except e.
Domain of fog: all real numbers x except
____ 36. Find ( f g )(x).
a.
b.
c.
d.
e.
____ 37. Find ( fg )(x).
a.
b.
c.
d.
e. ____ 38. Evaluate the indicated function for and . ( fg )(1) a. 12 b. –32 c. –20 d. –16 e. –30
____ 39. Find .
a.
b.
c.
d.
e.
____ 40. The monthly cost C of running the machinery in a factory for t hours is given by
The number of hours t needed to produce x products is given by
. Find the equation representing the cost C of manufacturing x products. a.
b.
c.
d.
e.
____ 41. Find the inverse function of f informally. a.
b.
c.
d.
e.
____ 42. Find the inverse function of .
a.
b.
c.
d.
e.
____ 43. Determine whether the function has an inverse function. If it does, find the inverse function.
a.
b.
c.
d.
e. No inverse ____ 44. Determine whether the function has an inverse function. If it does, find the inverse function.
a.
b.
c.
d.
e. No inverse
____ 45. Use the functions given by and to find .
a.
b.
c.
d.
e.
____ 46. Use the functions given by and to find .
a.
b. c.
d.
e.
____ 47. Use the functions given by and to find .
a.
b.
c.
d.
e.
____ 48. Use the graph of the function f to create a table of values for the given points. Then create a
second table that can be used to find . y
7
6
5
4
3
2
1
1 2 3 4 5 6 7 x a.
b.
c.
d. e.
____ 49. Graph the given function.
a. d. b. e.
c.
____ 50. Show algebraically that f and g are inverse functions.
a. Yes, f and g are inverse functions.
b. No, f and g are not inverse functions. Chapter 1 Test Review Answer Section
MULTIPLE CHOICE
1. ANS: C PTS: 1 REF: 1.5.25 2. ANS: D PTS: 1 REF: 1.5.27 3. ANS: B PTS: 1 REF: 1.5.79 4. ANS: D PTS: 1 REF: 1.5.95 5. ANS: C PTS: 1 REF: 1.5.125 6. ANS: E PTS: 1 REF: 1.5.126 7. ANS: C PTS: 1 REF: 1.5.127 8. ANS: A PTS: 1 REF: 1.5.128 9. ANS: B PTS: 1 REF: 1.5.52 OBJ: Determine intervals on which functions are increasing or decreasing 10. ANS: D PTS: 1 REF: 1.6.21 11. ANS: B PTS: 1 REF: 1.6.23 12. ANS: D PTS: 1 REF: 1.6.32 13. ANS: A PTS: 1 REF: 1.6.36 14. ANS: E PTS: 1 REF: 1.6.42 15. ANS: B PTS: 1 REF: 1.6.47 16. ANS: C PTS: 1 REF: 1.6.55 17. ANS: E PTS: 1 REF: 1.6.56 OBJ: Identify step functions 18. ANS: D PTS: 1 REF: 1.7.16b 19. ANS: A PTS: 1 REF: 1.7.19 20. ANS: D PTS: 1 REF: 1.7.24 21. ANS: D PTS: 1 REF: 1.7.25a 22. ANS: B PTS: 1 REF: 1.7.26c 23. ANS: C PTS: 1 REF: 1.7.45d 24. ANS: D PTS: 1 REF: 1.7.51c 25. ANS: C PTS: 1 REF: 1.7.61 26. ANS: D PTS: 1 REF: 1.7.65b 27. ANS: B PTS: 1 REF: 1.7.17 OBJ: Write equations for transformations of common functions 28. ANS: C PTS: 1 REF: 1.7.58 OBJ: Write equations for transformations of common functions 29. ANS: B PTS: 1 REF: 1.8.9b 30. ANS: B PTS: 1 REF: 1.8.11c 31. ANS: B PTS: 1 REF: 1.8.13a 32. ANS: B PTS: 1 REF: 1.8.18 33. ANS: E PTS: 1 REF: 1.8.21 34. ANS: B PTS: 1 REF: 1.8.37a 35. ANS: C PTS: 1 REF: 1.8.47a 36. ANS: D PTS: 1 REF: 1.8.13 OBJ: Find combinations of functions 37. ANS: C PTS: 1 REF: 1.8.14 OBJ: Find combinations of functions 38. ANS: D PTS: 1 REF: 1.8.23 OBJ: Evaluate combinations of functions 39. ANS: A PTS: 1 REF: 1.8.44b OBJ: Find compositions of functions 40. ANS: E PTS: 1 REF: 1.8.74a OBJ: Use compositions of functions to model real-life problems 41. ANS: E PTS: 1 REF: 1.9.10 42. ANS: D PTS: 1 REF: 1.9..51a 43. ANS: E PTS: 1 REF: 1.9.63 44. ANS: E PTS: 1 REF: 1.9.71 45. ANS: E PTS: 1 REF: 1.9.91 46. ANS: C PTS: 1 REF: 1.9.93 47. ANS: A PTS: 1 REF: 1.9.95 48. ANS: A PTS: 1 REF: 1.9.107 49. ANS: B PTS: 1 REF: 1.9.15a OBJ: Graph quadratic function 50. ANS: A PTS: 1 REF: 1.9.24a OBJ: Verify inverse functions