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# Calculus Concepts and Contexts 4th Edition Test bank James Stewart

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Section 1.3: New Functions From Old Functions

1. , then f(2x) is equal to
a. e.
b. f.
c. g.
d. h.

ANS: B PTS: 1

2. Let f(x) = and g(x) = . Find the domains of .
a. ( , 0] e. [ )
b. (2, ) f. ( , )
c. ( , 2) g. ( , ] [2, )
d. ( , 2) (2, ) h.

ANS: H PTS: 1

3. Let f(x) = and g(x) = . Find the domains of
a. [1, ) e. [ 3, 3]
b. [ , ] f. ( , 1] [1, )
c. ( , ] [ , ) g. ( , 1]
d. ( , 3] [3, ) h. [ , )

ANS: E PTS: 1

4. Let h(x) = sin x 3 sin x 4 and g(x) sin x. Find f(x) so that h(x)
a. f (x) = (3x + 2) e. f (x) = 3x 4x
b. f (x) = x + 3 f. f (x) = x 3x 4
c. f(x) = 3x 4 g. f (x) = x 4
d. f(x) = x 3x 4 h. f (x) = (x 4)

ANS: F PTS: 1

5. Let f(x) = 3x 2 and g(x) 2 3x. Find the value of (f g)(x) when x = 3..
a. 23 e. 3
b. 9 f. 6
c. 6 g. 9
d. 3 h. 23

ANS: A PTS: 1

6. Let f(x) = 2 x and g(x) 3 x. Find the value of when x = 5.
a. 510 e. 5
b. 5 f. 10
c. 2 g. 127
d. 0 h. 130

ANS: F PTS: 1

7. Let f(x) = x and . Find g(2).
a. 0 e. 8
b. 1 f. 16
c. 2 g. 32
d. 4 h. 64

ANS: E PTS: 1

8. Relative to the graph of y = x + 2, the graph of y = (x 2) 2 is changed in what way?
a. Shifted 2 units upward
b. Compressed vertically by a factor of 2
c. Compressed horizontally by a factor of 2
d. Shifted 2 units to the left
e. Shifted 2 units to the right
f. Shifted 2 units downward
g. Stretched vertically by a factor of 2
h. Stretched horizontally by a factor of 2

ANS: E PTS: 1

9. Relative to the graph of y = x , the graph of y = x 2 is changed in what way?
a. Shifted 2 units downward
b. Stretched horizontally by a factor of 2
c. Shifted 2 units to the right
d. Stretched vertically by a factor of 2
e. Compressed horizontally by a factor of 2
f. Compressed vertically by a factor of 2
g. Stretched vertically by a factor of 2
h. Stretched horizontally by a factor of 2

ANS: A PTS: 1

10. Relative to the graph of y = x , the graph of y = x is changed in what way?
a. Compressed horizontally by a factor of 2
b. Shifted 2 units downward
c. Stretched vertically by a factor of 2
d. Stretched horizontally by a factor of 2
e. Shifted 2 units upward
f. Compressed vertically by a factor of 2
g. Shifted 2 units to the right
h. Shifted 2 units to the left

ANS: F PTS: 1

11. Relative to the graph of y = x 2, the graph of y = 4x 2 is changed in what way?
a. Compressed vertically by a factor of 2
b. Stretched horizontally by a factor of 2
c. Compressed horizontally by a factor of 2
d. Shifted 2 units upward
e. Shifted 2 units to the right
f. Stretched vertically by a factor of 2
g. Shifted 2 units to the left
h. Shifted 2 units downward

ANS: C PTS: 1

12. Relative to the graph of y = sin x, the graph of y = 3 sin x is changed in what way?
a. Compressed horizontally by a factor of 3
b. Shifted 3 units to the right
c. Compressed vertically by a factor of 3
d. Shifted 3 units upward
e. Shifted 3 units to the left
f. Stretched vertically by a factor of 3
g. Shifted 3 units downward
h. Stretched horizontally by a factor of 3

ANS: F PTS: 1

13. Relative to the graph of y = e , the graph of y = is changed in what way?
a. Shifted 5 units upward
b. Shifted 5 units downward
c. Shifted 5 units to the right
d. Shifted 5 units to the left
e. Stretched horizontally by a factor of 5
f. Stretched vertically by a factor of 5
g. Compressed horizontally by a factor of 5
h. Compressed vertically by a factor of 5

ANS: D PTS: 1

14. Relative to the graph of y = sin x, where x is in the radians, the graph of y = sin x, where x is in degrees, is changed in what way?
a. Compressed horizontally by a factor of
b. Stretched vertically by a factor of
c. Compressed horizontally by a factor of
d. Stretched horizontally by a factor of
e. Compressed vertically by a factor of
f. Stretched vertically by a factor of
g. Stretched horizontally by a factor of
h. Compressed vertically by a factor of

ANS: G PTS: 1

15. Let f (x) = 8 + x . Find each of the following:

(a) f (2) f ( )

(b) f (x 2)

(c) [f (x)]

(d) f (x )

ANS:
(a) 24
(b)
(c)
(d)

PTS: 1

16. Let f (x) = . Find each of the following:

(a) f (0) f ( )

(b) f (x 2)

(c) [f (x)]

(d) f (x )

ANS:
(a) f (0) f ( ) = = 1
(b) f (x 2) = =
(c) [ f (x)] = 2x 5, x
(d) f (x ) =

PTS: 1

17. Let f (x) = . Find each of the following:

(a) f (0) f ( )

(b) f (x 2)

(c) [f (x)]

(d) f (x )

ANS:
(a) f (0) f ( ) = = 4 2 7.46
(b) f (x 2) = = = , x 2
(c) [ f (x)] = 16 x ,
(d) f (x ) = = , 0 x 2

PTS: 1

18. Let f (x) = , x . Find each of the following:

(a) f ( 1) f ( )

(b) f (x 3)

(c) f (x ) 3

(d) [f (x 3)]

ANS:
(a) f ( 1) f ( ) 1
(b) f (x 3) = , x
(c) f (x ) 3
(d.) , x 0

PTS: 1

19. Evaluate the difference quotient for f(x) .

ANS:

PTS: 1

20. Given the graph of y = f(x):

Sketch the graph of each of the following functions:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h) f

(i) 1

(j) 1

ANS:

PTS: 1

21. Use the graphs of f and g given below to estimate the values of f(g(x)) for x = , , , 0, 1, 2, and 3, and use these values to sketch a graph of y f(g(x)).

ANS:

x 3 2 1 0 1 2 3
f(g(x)) 0.5 3.88 3.50 2.88 3.50 3.88 .05

PTS: 1

22. f and g are functions defined by the following table.

x 3 2 1 0 1 2 3
f(x) 5 4 3 2 1 2 3
g(x) _4 1 1 2 1 1 4

Determine the following:

(a) (f g)(2)

(b) (f g)( 1)

(c)

(d)

(e)

(f)

(g)

(h)

ANS:
(a) 1
(b) 2
(c) 4
(d)
(e) 1
(f) 4
(g) 4
(h) 1

PTS: 1

23. Find functions f and g such that F(x) 1 2 cos x

ANS:
2x , g(x) = cos x is one possible answer. Answers will vary.

PTS: 1

24. Find functions f and g such that F(x) = 1 =

ANS:
f (x) = , g (x) = 1 cos x is one possible answer. Answers will vary.

PTS: 1

25. Find functions f and g such that F(x) = e =

ANS:
f (x) = e , g(x) sin x is one possible answer. Answers will vary.

PTS: 1

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