# Calculus: Early Transcendentals: Chapter 1 Early Transcendentals Flashcards

Set Details Share
created 4 years ago by jerryberry
327 views
updated 4 years ago by jerryberry
Subjects:
calculus, mathematics
Page to share:
Embed this setcancel
COPY
code changes based on your size selection
Size:
X

1

If f(x) = 3x + 1nx, find f-1(3)

1

2

Solve each equation for x

a) 1nx = 4

b)eex = 2

x = e4, x = ln(ln 2)

3

Simplify the expression

sin (2cos-14x)

8x√1-16x2

4

Fill in the blanks

Let f(x) = 5 + x2 + tan(πx/2), where -1 < x < 1

5,3

5

Determine whether f is even, odd, or neither

f(x) = 8x2/x4 + 1

even

6

Find the range of the function

h(x) = √4 - x2

0 ≤ h(x) ≤ 2

7

The graphs of f(x) and g(x)are given.
a) For what values of x is f(x) - g(x)?
b) Find the values of f(-2) and g(4) .

a) -2, 10
b) f(-2) = 6, g(4) = 2

8

A spherical balloon with radius r inches has volume 4/3 πr.
Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 1 inches.

4/3 π(3r2 + 3r + 1)

9

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in m2 of the caves by the equation S = 0.7A03
(a) The cave called mission impossible near puebla, mexico, has suface area of A = 90m2. How many species of bats would expect to find in that cave?
(b) If you discover that 5 species of bats live in cave estimate the area of the cave

a) 3 species
b) 702m2

10

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

F = 9/5 C + 32

Complete the table and find the slope.

(10,50)(-18,0);slope = 2

11

Plot the graph of the function in (a) the standard viewing window and (b) the indicated window

f(x) = x√7-x4, [-3, 3] X [-5,5]

12

Plot the graph of the function f in an appropriate viewing window.

f(x) = 2x3 - 5x2 + 4x + 27

13

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places.

f(x) = 0.3x2 - 1.1x - 3.5;

g(x) = -0.2x2 + 0.4x + 6.9

(-3.30104, 3.40021), (6.30104, 1.47979)

14

Determine whether f is one-to-one.

Yes

15

f(-4) = 19, f(0) = 3, f(1) = 1

16

Refer to the graph of the function f in the following figure.

a. Find f (3).
b. Find the value of x for which (i) f(x) = 1 and (ii) f(x) = 0.
c. Find the domain and range of f

a. 0
b. (i) 4 (ii) 3, 5
c. D: [3,6], R: [-3,1]

17

Let f(x) = x2 -6x + 7 and g(x) = √x+3, Find (g ⚬ f)(9)

√37

18

Find f ⚬ g ⚬ h if

f(x) = √x, g(x) = 7x + 4, and h(x) x2 - 4

√7x2-24

19

Let f(x) = x2 - 18x + 75 and g(x) = √x+7. Find (f ⚬ g)(74)(g ⚬ g)(74)

-6

20

Find the function g such that h(x) = (g ⚬ f)(x)

h(x) = sin5x and f(x) = sin x

g(x) = x5

21

Find all solutions of the equation correct to two decimal places.

√x = x3 - 4

1.75

22

Solve each equation for x

a) ln x = 6
b) eex = 2

x = e6, x = ln(ln 2)

23

Find the exact value of the expression.

tan(arcsin 1/2}

√3/3

24

Find the range of the function

h(x) = √25-x2

0≤h(x)≤5

25

Express the function in the form of f ⚬ g ⚬ h

H(x) = 3 - 6x3

h(x) = x3, g(x) = 6x, f(x) = 3 - x

26

Plot the graph of the function f in an appropriate viewing window.
f (x) = 5x4 – 3x3 + 3x2 – x + 26

27

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places.
f(x) = 0.3x2 – 1.2x – 3.4; g(x) = –0.2x2 + 0.2x + 6.3

(–3.22169, 3.57981), (6.02169, 0.25219)

28

Determine whether f is one-to-one.

No

29

The graph of f is given. Sketch the graph of f-1 on the same set of axes.

30

Find the inverse of f. Then sketch the graphs of f and f-1 on the same set of axes.

f(x) = cos-1(x/2), -2≤x≤2

f-1(x) = 2cos x, 0 ≤ x ≤ π

31

f(-1) = 9, f(0) = 8, f(1) = 1

32

Refer to the graph of the function f in the following figure.

a. Find f(0).
b. Find the value of x for which (i) f(x) = 1and (ii) f(x) = 0 .
c. Find the domain and range of f.

a. 0
b. (i) 1 (ii) 0, 2
c. D: [0, 3], R: [–3, 1]

33

Determine whether the function is even, odd, or neither.

f(x) = 2x2 + 9x

Neither

34

The following figure shows a portion of the graph of a function f defined on the interval [-1,1]. Sketch the complete graph of f if it is known f is odd.

35

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made. If the cardboard is 13 in. long and 9 in. wide and the square cutaways have dimensions of x in. by x in., find a function that gives the volume of the resulting box.

V = 4x3 - 44x2 + 117x

36

Use the vertical line test to determine whether the curve is the graph of a function of x.

Yes

37

Let f(x) = x2 - 18x + 80 and g(x) = √x+2. Find (g ⚬ f)(17)

√65

38

Find f ⚬ g ⚬ h if

f(x) = x-1/x+1, g(x) = 4√x, and h(x) = x + 1

39

Let f(x) = x2 - 14x + 38 and g(x) = √x+12. Find (f ⚬ f)(10)(g ⚬ g)(13)

70

40

Find the function g such that h(x) = (g ⚬ f)(x).

h(x) = 1/6x-5 and f(x) = 6x-5

g(x) = 1/x

41

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places.
f (x) = 0.5x3 – 1.8x2 + 2.2x – 4; = 2.8x – 4.

a. (–0.55126, –5.84352),
(3.87001, 6.53604)
b. (–0.55126, –1.54352)
(0.28124, 10.83604)
(3.87001, 0.78748)
c. (–0.55126, –1.54352)
(3.87001, 0.78748)
d. (–0.55126, –5.84352),
(0.28124, –3.51252)
(3.87001, 6.53604

d

42

Starting with the graph of y = ex, find the equation of the graph that results from reflecting about the line y = 3.

a. y = -ex
b. y = -ex + 6
c. y = -e-3x + 6
d. y = e-x +6
e. y = -ex+6

b

43

Use the Law of Exponents to rewrite and simplify the expression.

a

44

Starting with the graph of y = ex, write the equation of the graph that results from shifting 5 units right.

c

45

Suppose that the graph of y = log3x is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 2 ft? Rounded to the nearest mile.
a. 754.9 mi
b. 4,457,536.9 mi
c. 53,490,543 mi
d. 53,490,442.5 mi
e. 53,490,343 mi

b

46

Find the exact value of the given expression.
tan–1 1
a. 2π
b. π/4
c. 4/π
d.4π

b

47

Use the laws of logarithms to expand the expression.

b

48

Simplify the expression.

e3ln6

a. 9
b. 18
c. 216
d. 729

c

49

Find a formula for the inverse of the function.

y = ln(x + 6)

a. y = ex - 6
b. y = ex + 6
c. y = -6ex
d. y = 6ex
e. y = ex + 6

a

50

Find the exact value of the expression.

log5100 + log525 - 2log52

a. 7
b. 8
c. 6
d. 4
e. 5

d

51

The graphs of f(x) and g(x) are given. For what values of x is f(x) = g(x)?

e

52

Which of the following graphs is neither even nor odd?
a. f(x) = 4x2/x4+1
b. f(x) = 8x3 + 10x2 + 1
c. f(x) = x3 - 9x

b

53

A rectangle has perimeter 14m. Express the area of the rectangle as a function A(l) of the length of one of its sides.
a. A(l) = 7l - l2
b. A(l) = l - 7l2
c. A(l) = 14l - l2
d. A(l) = 14l + l2
e. A(l) = 7l + l2

a

54

What is the equation of this graph?

a. y = x8
b. y = x4
c. y = x2
d. y = 3√x
e.y = x7

e

55

Find the domain

d

56

Find the range of the function

e

57

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

F = 9/5 C + 32

What is the F-intercept and what does it represent

a. 9/5, Fahrenheit temperature corresponding to 0°C
b. 9/5, Celsius temperature corresponding to 32°C
c. 32, Celsius temperature corresponding to 0°F
d. 0, Fahrenheit temperature corresponding to 32°C
e. 32, Fahrenheit temperature corresponding to 0°C

e

58

If f(x) = x + 5 and h(x) = 4x - 10, find a function g such that g ⚬ f = h.
a. g(x) = 4x + 30
b. g(x) = 4x
c. g(x) = x - 30
d. g(x) = 4x - 30
e. g(x) = x + 30

d

59

The graph of the function f follows. Choose the graph of y = f(|x|)

d

60

Which of the following graphs is the graph of the function?

f(x) = sin |2x|

a. Graph 2
b. Graph 1
c. Graph 3

a

61

Find all solutions of the equation correct to two decimal places.

x3 - 9x2 - 100 = 0

a. x = 10
b. x = 0, x = 9.05
c. x = 0, x = 4.01, x = 9.05
d. x = -4.00, x = 9.05
e. x = 4.00, x = 9.05

a

62

Use the Law of Exponents to rewrite and simplify the expression.

b

63

Starting with the graph of y = ex, write the equation of the graph that results from shifting 3 units right.
a. y = 3ex - 3
b. y = ex + 3
c. y = ex + 3
d. y = ex - 3
e. y = ex - 3

e

64

Find the inverse function of f(x) = x+1/4x+1

e

65

Find f-1(a) for the function f and the real number a.

f(x) = x3 + x - 3; a = -1

a. 2
b. 1
c. 3
d. 0

b

66

Find the inverse of f. Then sketch the graphs of f and f-1 on the same set of axes.

f(x) = √4-x2, x ≥ 0

a

67

Find the exact value of the given expression

a. -1/2
b. 0
c. -√3/2
d. 1

b

68

Simplify the expression.

e2ln6

a. 12
b. 36
c. 8
d. 64

c

69

A box with an open top is to be constructed from a rectangular piece of card board with dimensions b = 9 in. by a = 24 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.

Express the volume V of the box as a function of x.
a. V(x) = 4x3 + 66x2 + 216x
b. V(x) = 4x3 + 33x2 + 196x
c. V(x) = 4x3 - 66x2 + 216x
d. V(x) = 4x3 - 33x2 + 196x
e. V(x) = 4x3 - 66x2 + 216x

b

70

A rectangle has perimeter 22m. Express the area of the rectangle as a function A(l) of the length l of one of its sides.
a. A(l) = 11l + l2
b. A(l) = 22l - l2
c. A(l) = 22l + l2
d. A(l) = 11l - l2
e. A(l) = l - 11l2

d

71

If f(x) = 4x2 + 2, find and simplify f(1+h)-f(1)/h , where h ≠ 0.
a. 4h
b. 2 + 4h2
c. 4 + 8h
d.8 + 4h

d

72

Find the domain and sketch the graph of the function. What is its range?

c

73

The graph of the function f is given. State the value of f(0).
a. f(0) = -10
b. f(0) = 5
c. f(0) = 10
d. f(0) = -5
e. f(0) = 0

d

74

What is the equation of this graph?
a. y = ∛x
b. y = x2
c. y = x7
d. y = x10
e. y = x8

c

75

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

F = 9/5 C + 32

What is the F-intercept and what does it represent?
a. 9/5, Fahrenheit temperature corresponding to 0° C
b. 9/5, Celsius temperature corresponding to 32° C
c. 32, Celsius temperature corresponding to 0° F
d. 0, Fahrenheit temperature corresponding to 32°
Ce. 32, Fahrenheit temperature corresponding to 0° C

e

76

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

y = 1 + 2x - x2

b

77

Suppose that the graph f is given. Describe how the graph of the function y = f(x - 3) - 3 can be obtained from the graph of f.
a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the right and 3 units up.
c. Shift the graph 3 units to the left and 3 units down.
d. Shift the graph 3 units to the left and 3 units up.
e. None of these

a

78

Which of the following graphs is the graph of the function?

f(x) = sin |3x|

a. Graph 3
b. Graph 1
c. Graph 2

c

79

Find the function f/g and its domain if f(x) = x/x-7 and g(x) = x/x+7.

a

80

The graph of the function f(x) = x2 - 9x + 5 has been compressed horizontally by a factor of 2. Find the function for the transformed graph.
a. g(x) = 4x2 - 18x + 5
b. g(x) = x2-9x+5/2
c. g(x) = 2x2 - 18x + 10
d. g(x) = x2-18x+20/4

a

81

Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the garden. Select the correct answer.

a.
b.
c.
d.

b

82

An open rectangular box with volume 2m3 has a square base. Express the surface area of the box as a function S(x) of the length x of a side of the base.

S(x) = x2 + 8/x

83

Determine whether f is even, odd, or neither. Select the correct answer.

f(x) = 4x2/x4+5

a. neither
b. odd
c. even

c

84

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her \$200 to drive 300mi and in July it cost her \$350 to drive 600mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

C = 0.5d + 50

85

If f(x) = x + 5 and h(x) = 4x - 10, find a function g such that g ⚬ f = h.

g(x) = 4x - 30

86

The graph of the function f follows. Choose the graph of y = f(|x|)

d

87

Sketch the graph of y = -1 - cos x over one period.

88

Find the function f g and its domain if f(x) = √x+7 and g(x) = √x-7 .

√x2-49

89

If a ball is thrown into the air with a velocity of 58ft/s, its height (in feet) after t seconds is given by

H = 58t - 9t2

Find the velocity when t = 9. Select the correct answer.
a. -101ft/s
b. -104ft/s
c. -106ft/s
d. -103ft/s
e. -99ft/s

b

90

The position of a car is given by the values in the following table.

t (seconds) 0, 1, 2, 3, 4
s (meters) 0, 21.9, 25.8, 69.2, 92.2

Find the average velocity for the time period beginning when t = 2 and lasting 2 seconds.

33.2 ft/s

91

Find the value of limx→0+ f(x). Select the correct answer.

f(x) = 1/1+61/x

a. 0
b. -0.7
c. -0.7
d. -0.6
e. 0.16

a

92

Find the vertical asymptotes of the function.

y = 8x2+1/9x-8x2

none of these

93

Find the limit limk→3 (h4 - 3h3 - 4h + 5)

-7

94

Find the limit limx→1 x2+x-2/x-1, if it exists. Select the correct answer.
a. 1
b. 3
c. 2
d. Does not exist

b

95

Evaluate the limit, if it exists.

limk→0 (x-h)6-x6/h

-6x5

96

Find the limit.

limx→2- x2-2x/x2-4x+4

-∞

97

Determine where f is discontinuous.

0 and 5

98

If f and g are continuous functions with f(9) = 6 and limx→9 [2f(x) - g(x)] = 9, find g(9).

a. g(9) = 21
b. g(9) = 15
c. g(9) = 12
d. g(9) = 24
e. g(9) = 3

e

99

How would you define f(7) in order to make f continuous at 7?

f(x) = x2-2x-3/x-7

f(7) = 12

100

Use the graph to determine where the function is discontinuous.

a. At 0
b. On the interval (0, 1)
c. At ±2.5
d. At 1

c

101

Plot the graph of the function f in an appropriate viewing window. Select the correct answer.

f(x) - x2/x2+8

a

102

Plot the graph of the function f in an appropriate viewing window.

f(x) = x + 0.02 sin 40x

103

Use the Law of Exponents to rewrite and simplify the expression.

a3/10b1/20

104

Starting with the graph of y = ex, find the equation of the graph that results from reflecting about the line y = 3. Select the correct answer.
a. y = -ex
b. y = ex + 6
c. y = -e-3x + 6
d. y = e-x + 6
e. y = -ex+ 6

b

105

Use the Law of Exponents to rewrite and simplify the expression.

x4nx5n+1/xn-5

x8n + 6

106

Starting with the graph of y = ex, write the equation of the graph that results from shifting 5 units right. Select the correct answer.
a. y = ex + 5
b. y = ex - 5
c. y = ex - 5
d. y = ex + 5
e.y = 5ex - 5

c

107

Find the inverse of f. Then sketch the graphs of f and f-1 on the same set of axes.
Select the correct answer.

f(x) = √4-x2, x ≥ 0

d

108

Solve the equation.

4ex + 5 = 2

x = ln 1/2 - 5

109

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by

Q(t) = Q0(1 - e-tla)

(The maximum charge capacity is Q0 and t is measured in seconds.) How long does it take to recharge the capacitor to 90% of capacity if a = 3?

-3ln(1/10) seconds

110

If f(x) = x2 - x + 6, evaluate the difference quotient f(a+h)-f(a)/h. Select the correct answer.
a.
b.
c.
d. h
e. none of these

e

111

A rectangle has perimeter 14m. Express the area of the rectangle as a function A(l) of the length l of one of its sides.

A(l) = 7l - l2

112

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

30

113

What is the equation of this graph?

y = x7

114

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function.

F = 9/5 C + 32

What is the F-intercept and what does it represent?

32, Fahrenheit temperature corresponding to 0°C

115

Classify the function as a Polynomial function, a Rational function, an algebraic function, or other.

f(x) = -8x-7 - x-5 - 7

Select the correct answer.
a. Other
b. Algebraic
c. Rational
d. Polynomial

c

116

Use the table to evaluate the expression (f ⚬ g)(6).

2

117

f(x)

118

Which of the following is the equation for the function g(x)? Select the correct answer.
a. g(x) = 4f(x)
b. g(x) = f(x) - 4
c. g(x) = -f(x + 4)
d. g(x) = f(x)/4
e. g(x) = -f(x) + 4

d

119

The graph of the function f(x) = x2 - 11x + 7 has been stretched horizontally by a factor of 2. Find the function for the transformed graph.

g(x) = x2-22x+28/4

120

Plot the graph of the function f in an appropriate viewing window.

f(x) = x3/x3+5

121

Plot the graph of the function f in an appropriate viewing window.

f(x) = x + 0.05sin50x

122

Starting with the graph of y = ex, find the equation of the graph that results from reflecting about the line y = 1. Select the correct answer.
a. y = e-x + 2
b. y = -e-lx + 2
c. y = -ex
d. y = -ex + 2
e. y = -ex + 2

d

123

Use the Law of Exponents to rewrite and simplify the expression.

x4nx5n+1/xn-3

x8n + 4

124

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is

n = f(t) = 100(2t/3)

When will the population reach 55,000? Round the answer to the nearest tenth.
Select the correct answer.
a. 22.3 hours
b. 27.3 hours
c. 32.3 hours
d. 37.3 hours
e. 17.3 hours

b

125

Find f-1(a) for the function f and the real number a. Select the correct answer.
f(x) = x3 + x - 1; a = -3
a. –2
b. –1
c. 1
d. 0

b

126

Find the exact value of the given expression.

sin-1 1/2

π/6

127

Use the laws of logarithms to expand the expression.

ln(x+4/x-5)1/2

1/2 ln (x + 4) - 1/2 ln (x - 5)

128

Simplify the expression. Select the correct answer.

e2ln5

a. 25
b. 32
c. 7
d. 10

a

129

If f(x) = x2 - x + 6, evaluate the difference quotient f(a+h)-f(a)/h.

none of these

130

A rectangle has perimeter 12m. Express the area of the rectangle as a function A(l) of the length l of one of its sides. Select the correct answer.
a. A(l) = l -6l2
b. A(l) = 12l - l2
c. A(l) = 6l - l2
d. A(l) = 6l + l2
e. A(l) = 12l + l2

c

131

Find the domain of the function f(x) = x/-5sinx+7

(-∞, ∞)

132

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program. Select the correct answer.
a. 20
b. 35
c. 54
d. 30
e. 38

d

133

An open rectangular box with volume 6m3 has a square base. Express the surface area of the box as a function S(x) of the length x of a side of the base.

S(x) = x2 + 24/x

134

Determine whether f is even, odd, or neither. Select the correct answer.

f(x) = 6x2/x4+3

a. neither
b. even
c. odd

b

135

Find the range of the function.

y = 4 + cos x

[3,5]

136

If f(x) = x + 5 and h(x) = 4x - 10, find a function g such that g ⚬ f = h.

g(x) = 4x - 30

137

The graph of the function follows. Choose the graph of y = |f(x)|

c

138

Suppose that the graph of is given f is given. Describe how the graph of the function y = f(x - 3) - 3 can be obtained from the graph of f. Select the correct answer.

a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the right and 3 units up.
c. Shift the graph 3 units to the left and 3 units up.
d. Shift the graph 3 units to the left and 3 units down.
e. None of these

a

139

Which of the following graphs is the graph of the function?

f(x) = sin|2x|

graph 2

140

Plot the graph of the function f in an appropriate viewing window.

f(x) = x4/x4+2

141

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. Select the correct answer.

f (x) = 0.5x3 – 1.8x2 + 2.2x – 4; g(x) = 2.8x – 4.3

a. (–0.55126, –5.84352),
(3.87001, 6.53604)
b. (–0.55126, –1.54352)
(0.28124, 10.83604)
(3.87001, 0.78748)
c. (–0.55126, –1.54352)
(3.87001, 0.78748)
d. (–0.55126, –5.84352),
(0.28124, –3.51252)
(3.87001, 6.53604)

d

142

The function f(x) = √4+cx2 is graphed below.

c > 0

143

Find the inverse function of f(x) = x+1/3x+1

f-1(x) = - x-1/3x-1

144

Determine whether the function is one-to-one.

f(x) = √4-x2

a. Yes
b. No

b

145

Find the exact value of the given expression.

tan-1 1

π/4

146

Use the laws of logarithms to expand the expression.

ln(x+5/x-6)1/2

1/2ln(x + 5) - 1/2ln(x - 6)

147

Simplify the expression. Select the correct answer.

e3ln6

a. 9
b. 18
c. 216
d. 729

c

148

Solve the equation

4ex + 5 = 2

x = ln 1/2 - 5

149

A box with an open top is to be constructed from a rectangular piece of card board with dimensions b = 4 in. by a = 28 in. by cutting out equal squares of side at each corner and then folding up the sides as in the figure.

Express the volume V of the box as a function of x.

V(x) = 4x4 -64x2 + 112x

150

Find an expression for the function y = f(x) whose graph is the bottom half of the parabola x + (6 - y)2 = 0. Select the correct answer.
a. y = 6 - √-x
b. y = 36 - √-x
c. y = 6 + √x
d. y = 36 - x2
e. y = 6 - x2

a

151

Find the domain of the function.

f(x) = 7x+1/x2

(-∞,0)∪(0,∞)

152

Find the domain and sketch the graph of the function. What is its range?

D: (-∞,∞)
R: (-∞,∞)

153

Find the domain. Select the correct answer.

g(u) = √u - √3-u

a. (0,3)
b. (-∞,0]
c. (-3,∞]
d. [0,3]
e.[0,∞)

d

154

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

y = 4 + 2x - x2

155

The graph of the function follows. Choose the graph of y = 1/2f(x - 1)

a

156

Sketch the graph of y = -1-cosx over one period.

157

Find the function f ⚬ g and its domain if f(x) = x-1/x and g(x) = x/x+3.

-3/x

D = (-∞,-3)∪(-3,0)∪(0,∞)

158

The graph of the function f(x) = x2 - 11x + 7 has been stretched horizontally by a factor of 2. Find the function for the transformed graph. Select the correct answer.
a. g(x) = x2-11x+7/2
b. g(x) = 2x2 - 22x + 14
c. g(x) = x2-22x+28/4
d. g(x) = 4x2 - 22x + 7

c