Download test bank for a graphical approach to algebra and trigonometry 5th edition by john hornsby lial rockswold

147 The graph of y = can be obtained from the graph of y = by vertically stretching by a factor of and reflecting across the -axis.. 153 The graph of y = is vertically stretched by a fac

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

Determine the intervals of the domain over which the function is continuous

A) (-∞, ∞) B) (-∞, 0); (0, ∞) C) (-∞, 0) D) (0, ∞)

Answer: A 4)

_

A) (-∞, 2] B) (-∞, 2); ( 2, ∞) C) ( 2, ∞) D) (-∞, ∞) Answer: A

A) (-∞, ∞) B) (-∞, 1); ( 1, ∞) C) (-∞, -1); ( -1,

∞)

D) (0, ∞) Answer: B

A) (-∞, ∞) B) (-∞, 2); ( 2, ∞) C) (-∞, 4); ( 4, ∞) D) (-∞, -2); ( -2,

∞) Answer: B

7)

4)

D) Increasing on [-1, ∞); Decreasing on (-∞, -1]

Answer: D

10)

7)

A) Increasing on (-∞, 0]; Decreasing on (-∞, 0]

B) Increasing on [0, ∞); Decreasing on (-∞, 0]

C) Increasing on (-∞, 0]; Decreasing on [0, ∞) D) Increasing on (∞, 0]; Decreasing on [0, -∞) Answer: B

A) Increasing on (∞, 0]; Decreasing on [0, -∞) B) Increasing on [0, ∞); Decreasing on (-∞, 0]

C) Increasing on (-∞, 0]; Decreasing on (-∞, 0]

D) Increasing on (-∞, 0]; Decreasing on [0, ∞) Answer: D

A) Increasing on (-∞, -3]; Decreasing on [ -3, ∞) B) Increasing on [-3, ∞); Decreasing on [ -3, ∞) C) Increasing on (-∞, -3]; Decreasing on (-∞, -3]

D) Increasing on [-3, ∞); Decreasing on (-∞, -3]

Answer: A

13)

10)

A) Increasing on (-∞, 0]; Decreasing on [0,

∞)

B) Increasing on [0, ∞); Decreasing on (-∞, 0]

Answer: D

A) Increasing on [ 4, ∞); Decreasing on [ -4, ∞); Constant on [ -4, 4]

B) Increasing on [ 4, ∞); Decreasing on (-∞, -4]; Constant on [ -4, 4]

C) Increasing on (-∞, 4]; Decreasing on (-∞, -4]; Constant on [4, ∞) D) Increasing on (-∞, 4]; Decreasing on [ -4, ∞); Constant on [4, ∞) Answer: B

A) Increasing on [1, 3]; Decreasing on [-2, 0] and [3, 5]; Constant on [2, 5]

B) Increasing on [-2, 0] and [3, 5]; Decreasing on [1, 3]; Constant on C) Increasing on [-1, 0] and [3, 5]; Decreasing on [0, 3]; Constant on [-5, -3]

D) Increasing on [-2, 0] and [3, 4]; Decreasing on [-5, -2] and [1, 3]

Answer: B

13)

16) 16)

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]

D: , R: (-∞, 0]

D) D: [0, ∞), R:

Answer: A

18)

Answer: B

22) 22)

A) D: (-∞, 3) ∪ (3, ∞), R: (-∞, 1) ∪ (1, ∞) B) D: (0, ∞), R: (1, ∞) C) D: (-∞, ∞), R: (-∞, ∞) D) D: (-∞, -3) ∪ (-3, ∞), R: (-∞, ∞) Answer: A

A) D: (-∞, 4) ∪ (4, ∞), R: (-∞, 2) ∪ (2, ∞) B) D: (-∞, ∞), R: (-∞, ∞) C) D: (-∞, -2) ∪ (-2, ∞), R: (-∞, -4) ∪ (-4, ∞) D) D: (-∞, 2) ∪ (2, ∞), R: (-∞, 4) ∪ (4, ∞) Answer: D

Answer: C

Based on the ordered pairs seen in the pair of tables, make a conjecture as t o whether the function defined in Y1 is

even, odd, or neither even nor odd

Answer: A

41)

A) Even B) Neither even nor odd C) Odd Answer: A

A) Neither even nor odd B) Odd C) Even Answer: C

A) Neither even nor odd B) Odd C) Even Answer: B

Answer: A

71)

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

73) Complete the right half of the graph of y = f(x) for each of the following conditions:

(i) f is odd

(ii) f is even

73) A)

Answer: (i) f is odd

(ii) f is even

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

Write an equation that results in the indicated translation

74)

y = Answer: B

A) y = B) y = + 6 C) y = D) y = - 6 Answer: A

76) The absolute value function, shifted 6 units upward 76) A) y =

A) y = - 5 B) y = C) y = D) y = + 5 Answer: D

The function Y2 is defined as Y1 + k for some real number k Based upon the given information about Y1 and Y2, find

99)

A) (-∞, ∞); [ - 8, ∞) B) (-∞, ∞); (-∞, ∞) C) (-∞, ∞); [0, ∞) D) [ - 8, ∞); (-∞, ∞) Answer: A

102)

99)

y = - 6

_

A) (-∞, ∞); (-∞, ∞) B) [ 6, ∞); (-∞, ∞) C) (-∞, ∞); [ 2, ∞) D) [0, ∞); [0, ∞) Answer: A

by hand Do not use a calculator

C) 102)

D) Answer: A

Answer: C

D) Answer: A

Answer: A

D) Answer: B

Answer: A

113) y = - 1 113)

Answer: B

that defines the function

114)

A) y = - 5 B) y =

_

+ Answer: D

_

A) y = + 5 B) y = C) y = D) y =

+ 3 Answer: B

A) y = - 3 B) y = - 3 C) y = D) y = Answer: A

A) y =

- 6 B) y = C) y = D) y = -6

Answer: A

Find the linear equation that meets the stated criteria

120) The linear equation y = 241x + 6320 provides an approximation of the annual cost (in dollars) to

rent an apartment at the Leisure Village Retirement Community, where x = 1 represents 1978, x

= 2 represents 1979, and so on Write an equation that yields the same y-values when the exact

year number is entered

A) y = 241( 1977 - x) + 6320 B) y = 241(x - 1977) + 6320

120) 117)

C) y = 241( 1978 - x) + 6320 D) y = 241(x - 1978) + 6320 Answer: B

121) The linear equation y = 480x + 3420 provides an approximation of the annual cost (in dollars) of

health insurance for a family of three, where represents 1986, represents 1987,

and so on Write an equation that yields the same y-values when the exact year number is

entered

A) y = 480(x - 1985) + 3420 B) y = 480( 1986 - x) + 3420 C) y = 480(x - 1986) + 3420 D) y = 480( 1985 - x) + 3420 Answer: A

122) The linear equation y = 71.61x + 1023 provides an approximation of the value (in dollars) of

an account opened on January 1, 1992, in the amount of $ 1023 and earning 7% simple interest,

where x = 0 represents January 1, 1992, x = 1 represents January 1, 1993, x = 2 represents

January 1, 1994, and so on Write an equation that yields the same y-values when the exact year

number is entered

A) y = 71.61( 1993 - x) + 1023 B) y = 71.61(x - 1993) + 1023 C) y = 71.61( 1992 - x) + 1023 D) y = 71.61(x - 1992) + 1023 Answer: D

123) The table shows the number of members in the Windy City Edsel Owners Club during the years

1980-1984

Use a calculator to find the least squares regression line for this data, where x = 0 represents

1980, x = 1 represents 1981, and so on

A) y = 8.1x + 59 B) y = 8.5x + 62 C) y = 7.9x + 63 D) y = 8.3x + 61 Answer: B

124) The table shows the number of members in the Windy City Edsel Owners Club during the years

1986-1990

Use a calculator to find the least squares regression line for this data, where x = 0 represents

1986, x = 1 represents 1987, and so on

A) y = 28.3x + 106 B) y = 27.6x + 111 C) y = 28.4x + 105 D) y = 28.1x + 109 Answer: D

121)

122)

123)

124)

Provide an appropriate response

125) Explain how the graph of g(x) = f(x) - 8 is obtained from the graph of y = f(x) 125) A) Shift the graph of f to the left 8 units B) Shift the graph of f to the right 8 units

C) Shift the graph of f downward 8 units D) Shift the graph of f upward 8 units

128) The graph shown is a translation of the function The graph shown is of the form

What are the values of h and k?

A) h = -4, k = 3 B) h = 4, k = 3 C) h = -4 k = -3 D) h = 4, k = -3 Answer: B

128)

129) Sketch the graph of y = f(x - 3) for the given graph of y = f(x) 129)

A)

D) Answer: C

131) Use the graph of y = f(x) to find the x-intercepts of the graph of y = f(x + 2) 131)

Answer: A

Write the equation that results in the desired transformation

A) y = - 1 B) y = C) y = - D) y = Answer: C

B) y = 0 8 C) y = D) y =

135) The squaring function, vertically stretched by a factor of 7 and reflected across the x-axis 135)

7) Answer: B

136) The absolute value function, vertically stretched by a factor of 4.9 and reflected across the x-axis 136)

;

A) y = B) y = C) y = D) y = -4.9 Answer: D

137) The absolute value function, vertically stretched by a factor of 7.3 and reflected across the y-axis 137)

g

; x

on

; x

Fill in each blank with the appropriate response

147) The graph of y = can be obtained from the graph of y = by vertically stretching by a

factor of and reflecting across the -axis

Answer: A

148) The graph of y = can be obtained from the graph of y = by vertically stretching by a

factor of and reflecting across the -axis

Answer: D

149) The graph of y = + 7 can be obtained from the graph of y = by shifting

horizontally units to the , vertically stretching by a factor of reflecting across the

-axis, and shifting vertically units in the direction

A) 4; right; 7; x; 6; upward B) 4; left; 6; x; 7; upward C) 4; right; 7; y; 6; downward D) 4; right; 6; x; 7; upward Answer: D

150) The graph of y = - 7 can be obtained from the graph of y = by shifting

horizontally units to the , vertically stretching by a factor of reflecting across the

-axis, and shifting vertically units in the direction

A) 2; right; 6; x; 7; downward B) 2; left; 6; x; 7; downward C) 2; right; 6; x; 7; upward D) 2; left; 7; x; 6; downward Answer: B

The graph of y = - - 8 can be obtained from the graph of y = by shifting

horizontally units to the , vertically shrinking by a factor of reflecting across the

-axis, and shiftin vertically units in the directi

151)

A) 3; left; 8 ; ; downward C)

3; right; ; x; 8; upward

B) 3; left; ; 8; downward D)

3; right; ; x; 8; downward 152)

Answer: B

The graph of y = - + 2 can be obtained from the graph of y = by reflecting across the

-axis, vertically shrinking by a factor of reflecting across the -axis, and shifting

vertically units in the direction

152)

A) x; 2; y; ; upward C)

y; ; x; 2; upward

B) x; ; x; 2; upward D)

y; ; x; 2; downward Answer: C

Give the equation of the function whose graph is described

153) The graph of y = is vertically stretched by a factor of 9, and the resulting graph is reflected acros x-axis

s the

154) The graph of y = is shifted 2 units to the right This graph is then vertically stretched by a

factor of 6 and reflected across the x-axis Finally, the graph is shifted 8 units upward

A) y = -6

C) y = -6 Answer: C

155) The graph of y = is shifted 4 units to the left This graph is then vertically stretched by a

factor of 5 and reflected across the x-axis Finally, the graph is shifted 7 units downward

156) The graph of y = is shifted 2 units to the left This graph is then vertically shrunk by a factor

of and reflected across the x-axis Finally, the graph is shifted 8 units downward

The graph of y = is reflected across the y-axis and vertically shrunk by a factor of This

graph is then reflected across the x-axis Finally, the graph is shifted 4 units upward

Answer: A

7.9

D) y = 0 1 + 7.9

159) The graph of y = is vertically stretched by a factor of 6.6 This graph is then reflected across

the x-axis Finally, the graph is shifted 0.32 units downward

_

D) y = +

10

161)

The graph of y = is shifted 7.8 units to the left This graph is then vertically stretched by a

factor of 8.1 Finally, the graph is reflected across the x-axis

161)

A)

y = -8.1 C)

y = 8.1 Answer: A

B)

y = -8.1 D)

y = -7.8

The graph of the given function is drawn with a solid line The graph of a function, g(x), transformed from this one is

drawn with a dashed line Find a formula for g(x)

A) g(x) = - 2 B) g(x) = C) g(x) = D) g(x) = Answer: B

A)

164)

Answer: C

164)

C) g(x) = -

C) D)

Answer: D

A)

D) Answer: A

Use the accompanying graph of y = f(x) to sketch the graph of the indicated function

D) Answer: A

Answer: A

D) Answer: A

Answer: A

Let f be a function with the given domain and range Find the domain and range of the indicated function

_

A) Increasing on (-∞, -1]; Decreasing on [-1, ∞) B) Increasing on [-1, ∞); Decreasing on (-∞, -1]

C) Increasing on [1, ∞); Decreasing on (-∞, 1]

D) Increasing on (-∞, 1]; Decreasing on [1, ∞) Answer: B

A) Increasing on (-∞, 0]; Decreasing on (-∞, 0]

B) Increasing on (-∞, 0]; Decreasing on [0, ∞) C) Increasing on (∞, 0]; Decreasing on [0, -∞) D) Increasing on [0, ∞); Decreasing on (-∞, 0]

Answer: D

A) Increasing on (-∞, 0]; Decreasing on (-∞, 0]

B) Increasing on (-∞, 0]; Decreasing on [0, ∞) C) Increasing on (∞, 0]; Decreasing on [0, -∞) D) Increasing on [0, ∞); Decreasing on (-∞, 0]

Answer: B

194)

191)

_

A) Increasing on (-∞, 4]; Decreasing on [ 4, ∞) B) Increasing on [4, ∞); Decreasing on (-∞, 4]

C) Increasing on [4, ∞); Decreasing on [ 4, ∞) D) Increasing on (-∞, 4]; Decreasing on (-∞, 4]

Answer: C

A) Increasing on [ 4, ∞); Decreasing on (-∞, -4]; Constant on [ -4, 4]

B) Increasing on (-∞, 4]; Decreasing on [ -4, ∞); Constant on [4, ∞) C) Increasing on [ 4, ∞); Decreasing on [ -4, ∞); Constant on [ -4, 4]

D) Increasing on (-∞, 4]; Decreasing on (-∞, -4]; Constant on [4, ∞) Answer: A

197)

194)

_

A) Increasing on [1, 3]; Decreasing on [-2, 0] and [3, 5]; Constant on [2, 5]

B) Increasing on [-1, 0] and [3, 5]; Decreasing on [0, 3]; Constant on [-5, -3]

C) Increasing on [-2, 0] and [3, 4]; Decreasing on [-5, -2] and [1, 3]

D) Increasing on [-2, 0] and [3, 5]; Decreasing on [1, 3]; Constant on Answer: D

A) Increasing on [-3, 0]; Decreasing on [-5, -3) and [2, 5]; Constant on [0, 2]

B) Increasing on [-3, -1]; Decreasing on [-5, -2] and [2, 4]; Constant on [-1, 2]

C) Increasing on [-5, -3] and [2, 5]; Decreasing on [-3, 0]; Constant on [0, 2]

D) Increasing on [-3, 1]; Decreasing on [-5, -3] and [0, 5]; Constant on [1, 2]

Answer: A

Shown here are graphs of y1 and y2 The point whose coordinates are given at the bottom of the screen lies on the

graph of y1 Use this graph, and not your own calculator, to find the value of y 2 for the same value of x shown

197)

A) -8 B) -2 C) -32 D) 2 Answer: A

207)

204)

- 3

_

A) g(x) = (-x + 6)2 B) g(x) = -x2 - 6 C) g(x) = (-x - 6)2 D) g(x) = -x2 + 6 Answer: A

A) g(x) = x2 + 5

B) g(x) = x2 - 5

C) g(x) = (x + 5)2 D)

g(x) = (x - 5)2 Answer: D

D) g(x) = (x2 - 3)

210)

207)

_

A) g(x) = -x2 - 4 B) g(x) = -x2 + 4 C) g(x) = D) g(x) = -(x + 4)2 Answer: D

Provide an appropriate response

211) True or false? If r is an x-intercept of the graph of y = f(x), then has an x-intercept at x =

213) True or false? If the function y = f(x) increases on the interval (a, b) of its domain, then y =

f(-x) increases on the interval (a, b)

215) True or false? If the function y = f(x) increases on the interval (a, b) of its domain, and we are

given that c < 0, then the graph of decreases on the interval

Answer: A

216) True or False If the graph of y = f(x) is symmetric with respect to the then the graph of

y = f(-x) is symmetric with respect to the y-axis

7) True or False If the graph of y = f(x) is symmetri c with respect to the origin, the n the graph of y 217)

= -f(x) is symmetric with respect to the origin

A) True Answer: A

B) False