Test bank for precalculus concepts through functions a right triangle approach to trigonometry 3rd edition by sullivan

He leaves home, walks 5 blocks in 15 minutes at a constant speed, and realizes that he forgot his wallet at home.. So Michael runs back in 10 minutes.. At home, ittakes him 3 minutes to

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3→ 12

6 → 24

9→ 36

12 → 48A) functiondomain: {3, 6, 9, 12}

range: {12, 24, 36, 48}

B) functiondomain:{12, 24, 36, 48}

snakecatdogA) functiondomain: {Alice, Brad, Carl}

range: {snake, cat, dog}

B) functiondomain: {snake, cat, dog}

catdog

A) functiondomain: {Alice, Brad, Carl}

range: {cat, dog}

B) functiondomain: {cat, dog}

range: {Alice, Brad, Carl}

C) not a function

4) {(-1, -8), (1, 4), (4, 0), (6, -2)}

A) functiondomain: {-1, 1, 4, 6}

range: {-8, 4, 0, -2}

B) functiondomain: {-8, 4, 0, -2}

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7) {(6.55, 7.65), (6.555, -7.6), (2

3 , 0), (0.67, -6)}

A) functiondomain: {6.55, 6.555, 2

3 , 0.67}

range: {7.65, -7.6, 0, -6}

B) functiondomain: {7.65, -7.6, 0, -6}

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A) -3x2 - 2x + 4 B) 3x2 - 2x - 4 C) 3x2 - 2x + 4 D) -3x2 - 2x - 48) Find -f(x) when f(x) = |x| - 5.

Full file at https://TestbankDirect.eu/

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13) Find f(x + h) when f(x) = 2x2 - 2x + 2.

A) 2x2 + 4xh + 2h2 - 2x - 2h + 2 B) 2x2 + 2h2 - 2x - 2h + 2C) 2x2 + 2h2 + 2x + 2h + 2 D) 2x2 + 2xh + 2h2 - 2x - 2h + 2

14) Find f(x + h) when f(x) = 5x + 8

9x - 2.A) 5x + 5h + 8

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5) h(x) = x - 4

x3 - 49xA) {x|x ≠ -7, 0, 7} B) {x|x ≠ 0} C) {x|x ≠ 4} D) all real numbers

6) f(x) = 16 - x

7) x

x - 10A) {x|x > 10} B) {x|x ≥ 10} C) {x|x ≠ 10} D) all real numbers

2) f(x) = 8x - 2; g(x) = 5x - 9

Find f - g

A) (f - g)(x) = 3x + 7; all real numbers B) (f - g)(x) = 3x - 11; {x|x ≠ 11

3 }C) (f - g)(x) = 13x - 11; {x|x ≠ 1} D) (f - g)(x) = -3x - 7; all real numbers

g)(x) = 4x + 5

5x - 2; {x|x ≠ 25 } B) (f

g)(x) = 4x + 55x - 2; {x|x ≠ - 54 }C) (f

g)(x) =

5x - 24x + 5; {x|x ≠

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6) f(x) = x + 9; g(x) = 3x2

Find f - g

A) (f - g)(x) = -3x2 + x + 9; all real numbers B) (f - g)(x) = 3x2 - x - 9; all real numbersC) (f - g)(x) = -3x2 + x + 9; {x|x ≠ -9} D) (f - g)(x) = 3x2 + x + 9; all real numbers

7) f(x) = 2x3 + 3; g(x) = 6x2 + 1

Find f · g

A) (f · g)(x) = 12x5 + 2x3 + 18x2 + 3; all real numbersB) (f · g)(x) = 12x6 + 2x3 + 18x2 + 3; all real numbersC) (f · g)(x) = 12x5 + 2x3 + 18x2 + 3; {x|x ≠ 0}

D) (f · g)(x) = 2x3 + 6x2 + 3; all real numbers8) f(x) = x; g(x) = 3x - 4

Find f

g.A) (f

g)(x) = x

3x - 4; {x|x ≥ 0, x ≠ 43 } B) (f

g)(x) = x

3x - 4; {x|x ≠ 43 }C) (f

5

6 }C) (f - g)(x) = 3x - 1

6x - 5; {x|x ≠ 56 , x ≠ 13 } D) (f - g)(x) = 3x - 1

6x - 5; {x|x ≠ 0}

11) f(x) = x + 11; g(x) = 5

xFind f · g

Trang 8

-5

-10

A) functiondomain: {x|x ≤ -2 or x ≥ 2}

range: all real numbersintercepts: (-2, 0), (2, 0)symmetry: x-axis, y-axis, origin

B) functiondomain: all real numbersrange: {y|y ≤ -2 or y ≥ 2}

intercepts: (-2, 0), (2, 0)symmetry: y-axisC) function

domain: {x|-2 ≤ x ≤ 2}

range: all real numbersintercepts: (-2, 0), (2, 0)symmetry: x-axis, y-axis

D) not a function

Trang 9

x

y 5

-5

x

y 5

-5

A) functiondomain: {x|x > 0}

range: all real numbersintercept: (1, 0)

symmetry: none

B) functiondomain: {x|x > 0}

symmetry: originC) function

domain: all real numbersrange: {y|y > 0}

intercept: (1, 0)symmetry: none

D) not a function

3)

x - -34 -2 -4 4 2 34 

y 1

-1

x - -34 -2 -4 4 2 34 

y 1

-1

A) functiondomain: {x|-π ≤ x ≤ π}

B) functiondomain: {x|-1 ≤ x ≤ 1}

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x

y 10

5

-5

-10

A) functiondomain: all real numbersrange: {y|y ≤ 9}

intercepts: (-2, 0), (0, 8), (4, 0)symmetry: none

B) functiondomain: {x|x ≤ 9}

range: all real numbersintercepts: (-2, 0), (0, 8), (4, 0)symmetry: y-axis

C) functiondomain: all real numbersrange: {y|y ≤ 9}

intercepts: (0, -2), (8, 0), (0, 4)symmetry: none

5

-5

-10

A) functiondomain: {x|-3 ≤ x ≤ 3}

range: {y|-3 ≤ y ≤ 3}

intercepts: (-3, 0), (0, -3), (0, 3), (3, 0)symmetry: x-axis, y-axis, origin

B) functiondomain: {x|-3 ≤ x ≤ 3}

range: {y|-3 ≤ y ≤ 3}

intercepts: (-3, 0), (0, -3), (0, 3), (3, 0)symmetry: x-axis, y-axis

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x

y 5

-5

x

y 5

-5

A) functiondomain: {x|x ≥ -2}

range: {y|y ≥ 0}

intercepts: (-2, 0), (0, 2), (2, 0)symmetry: none

B) functiondomain: {x|x ≥ 0}

range: {y|y ≥ -2}

intercepts: (-2, 0), (0, 2), (2, 0)symmetry: y-axis

C) functiondomain: all real numbersrange: all real numbersintercepts: (-2, 0), (0, 2), (2, 0)symmetry: none

5

-5

-10

A) functiondomain: all real numbersrange: {y|y = 5 or y = 4}

intercept: (0, 4)symmetry: none

B) functiondomain: {x|x = 5 or x = 4}

symmetry: x-axis

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8) What are the x-intercepts?

50

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A) 164.77 pounds B) 7.72 pounds C) 165.23 pounds D) 165 pounds

C)

y y

D)

y y Full file at https://TestbankDirect.eu/

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Solve the problem.

28) Michael decides to walk to the mall to do some errands. He leaves home, walks 5 blocks in 15 minutes at a

constant speed, and realizes that he forgot his wallet at home. So Michael runs back in 10 minutes. At home, ittakes him 3 minutes to find his wallet and close the door. Michael walks 5 blocks in 15 minutes and thendecides to jog to the mall. It takes him 10 minutes to get to the mall which is 5 blocks away. Draw a graph ofMichaelʹs distance from home (in blocks) as a function of time

y y Full file at https://TestbankDirect.eu/

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29) A steel can in the shape of a right circular cylinder must be designed to hold 750 cubic centimeters of juice (see

figure). It can be shown that the total surface area of the can (including the ends) is given by S(r) = 2πr2 + 1500

r ,where r is the radius of the can in centimeters. Using the TABLE feature of a graphing utility, find the radiusthat minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10 Full file at https://TestbankDirect.eu/

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x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

3)

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

4)

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10 Full file at https://TestbankDirect.eu/

Trang 21

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

6)

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

x -10 -8 -6 -4 -2 2 4 6 8 10

y 10 8 6 4 2

-2 -4 -6 -8 -10

7)

x - -2 2 

y 5 4 3 2 1

-1 -2 -3 -4 -5

x - -2 2 

y 5 4 3 2 1

-1 -2 -3 -4 -5

Trang 22

x - -2 2 

y 5 4 3 2 1

-1 -2 -3 -4 -5

x - -2 2 

y 5 4 3 2 1

-1 -2 -3 -4 -5

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x

y 5

-5

x

y 5

-5

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3) (0, 1)

x

y 5

-5

x

y 5

-5

x

y 5

5

-5 Full file at https://TestbankDirect.eu/

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6) (-2, 0)

x

y 10

5

-5

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9) (-2, -1)

x

y 3

(0.5, 1.5) (3.5, 1.5)

(-2.5, 0)

(-1, -1) (0, -1)

(2, 0) Full file at https://TestbankDirect.eu/

Trang 27

12) (5, ∞)

x

y 10

-10

(-8, 5)

(-5, 0)

(0, 0) (4, 0)

(5, -2.5) (-9.5, 0)

-10

(-8, 5)

(-5, 0)

(0, 0) (4, 0)

(5, -2.5) (-9.5, 0)

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A) Increasing on (-∞, ∞) B) Decreasing on (-∞, 0); increasing on (0, ∞)C) Decreasing on (-∞, ∞) D) Increasing on (-∞, 0); decreasing on (0, ∞)15)

D) Increasing on (-∞, ∞)

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A) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2)B) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1)

C) Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1)D) Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2)

y 5 4 3 2 1

-1 -2 -3 -4 -5

x -5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

A) f has a local maximum at x = 0; the local maximum is 2B) f has a local maximum at x = -1 and 1; the local maximum is 0C) f has a local maximum at x = 1; the local maximum is 2D) f has no local maximum

Trang 30

2) Find the numbers, if any, at which f has a local minimum. What are the local minima?

x -5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

x -5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

A) f has a local minimum at x = -1 and 1; the local minimum is 0B) f has a local minimum at x = 0; the local minimum is 3C) f has a local minimum at x = -1; the local minimum is 0D) f has no local minimum

3) Find the numbers, if any, at which f has a local maximum. What are the local maxima?

x - -2 2 

y 2

1

-1

-2

x - -2 2 

y 2

1

-1

-2

A) f has a local maximum at x = 0; the local maximum is 1B) f has a local maximum at x = -π and π; the local maximum is -1C) f has a local maximum at -π; the local maximum is 1

D) f has no local maximum

Trang 31

4) Find the numbers, if any, at which f has a local minimum. What are the local minima?

x - -2 2 

y 2

1

-1

-2

x - -2 2 

y 2

1

-1

-2

A) f has a local minimum at x = 0; the local minimum is -2B) f has a local minimum at x = -π and π; the local minimum is 2C) f has a local minimum at x = -π; the local minimum is -2D) f has no local minimum

5)

x

y 10

-10

(-8, 5)

(-5, 0)

(0, 0) (4, 0)

(5, -2.5) (-9.5, 0)

-10

(-8, 5)

(-5, 0)

(0, 0) (4, 0)

(5, -2.5) (-9.5, 0)

Trang 32

6) The height s of a ball (in feet) thrown with an initial velocity of 60 feet per second from an initial height of 8 feet

is given as a function of time t (in seconds) by s(t) = -16t2 + 60t + 8. What is the maximum height? Round to thenearest hundredth, if necessary

x

y

x y

Trang 33

A) Absolute maximum: f(3) = 6; Absolute minimum: noneB) Absolute maximum: f(3) = 6; Absolute minimum: f(5) = 1C) Absolute maximum: f(7) = 4; Absolute minimum: f(0) = 2D) Absolute maximum: f(3) = 6; Absolute minimum: f(0) = 23)

A) Absolute maximum: none; Absolute minimum: f(1) = 2B) Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2C) Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2D) Absolute maximum: none; Absolute minimum: none

Trang 34

A) Absolute maximum: none; Absolute minimum: noneB) Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2C) Absolute maximum: none; Absolute minimum: f(1) = 2D) Absolute maximum: f(4) = 7; Absolute minimum: none

B) local maximum at (1, -1)local minimum at (-1, 3)increasing on (-2, -1) and (1, 2)decreasing on (-1, 1)

C) local maximum at (-1, 3)local minimum at (1, -1)increasing on (-1, 1)decreasing on (-2, -1) and (1, 2)

D) local maximum at (1, -1)local minimum at (-1, 3)increasing on (-2, -1)decreasing on (-1, 1)

Trang 35

7) f(x) = 2 + 8x - x2; (-5, 5)

A) local maximum at (4, 18) B) local minimum at (4, 50)C) local minimum at (-4, 18) D) local maximum at (-4, 50)8) f(x) = x3 - 3x2 + 1; (-5, 5)

A) local maximum at (0, 1)local minimum at (2, -3) B) local minimum at (0, 1)local maximum at (2, -3)

9) f(x) = x3 - 12x + 2; (-5, 5)

A) local maximum at (-2, 18)local minimum at (2, -14) B) local maximum at (-2, 18)local minimum at (0, 0)

local minimum at (2, -14)

10) f(x) = x4 - 5x3 + 3x2 + 9x - 3; (-5, 5)

A) local minimum at (-0.57, -6.12)local maximum at (1.32, 5.64)local minimum at (3, -3)

B) local minimum at (-1, -6)local maximum at (1, 6)local minimum at (3, -3)C) local minimum at (-3, -3)

local maximum at (-1.32, 5.64)local minimum at (0.57, -6.12)

D) local minimum at (-0.61, -5.64)local maximum at (1.41, 6.12)local minimum at (3, -3)

Trang 36

A) 1

310

9) f(x) = x - 23 ; from 4 to 7

A) - 3

13

1612) f(x) = x3 + x2 - 8x - 7; from 0 to 2

1613) f(x) = 2x - 1; from 1 to 5

Trang 37

16) f(x) = 3

x + 2A) y = - 1

17) f(x) = x + 15

A) y = ( 17 - 4)x - 17 + 8 B) y = (- 17 + 4)x + 17 - 8C) y = ( 17 - 4)x + 17 - 8 D) y = (- 17 - 4)x - 17 + 8

C) absolute value function D) reciprocal function3)

Trang 39

x

y 5

-5

x

y 5

-5

x

y 5

-5

C)

y 5

D)

y 5

y 5 Full file at https://TestbankDirect.eu/

Trang 40

10) f(x) = x2

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 41

11) f(x) = x3

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 42

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 43

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 44

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 45

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 46

16) f(x) = 4

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 47

x

y 5

-5

x

y 5

-5

x

y 5

x

y 5

D)

x

y 5

x

y 5 Full file at https://TestbankDirect.eu/

Trang 48

f(x) = -x + 3 if x < 22x - 3 if x ≥ 2

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 49

x

y 5

-5

x

y 5

-5

x

y 5

-5

x

y 5

Trang 50

f(x) =

x + 2 if -9 ≤ x < 5-9 if x = 5-x + 7 if x > 5

x

y 10

5

-5

-10 (-9, -7)

5

-5

-10 (-9, -7)

(5, 7)

(5, -9) (5, 2)

B)

x

y 10

5

-5

-10 (-9, -7)

5

-5

-10 (-9, -7)

(5, 7)

(5, -9) (5, 2)

C)

x

y 10

5

-5

(5, 8)

(5, 2) Full file at https://TestbankDirect.eu/

Trang 51

f(x) =

1 if -3 ≤ x < 3

|x| if 3 ≤ x < 93

x if 9 ≤ x ≤ 13

x

y 10

5

-5

-10 (-3, -1) (3, -1)

5

-5

-10 (-3, -1) (3, -1)

5

-5

-10 (-3, -1) (3, -1)

5

-5

-10 (-3, -1) (3, -1)

(3, 3)

(9, 9)

(9, 2.1)

(13, 2.4) Full file at https://TestbankDirect.eu/

Trang 52

y 10

5

-5

-10 (0, -8)

x

y 10

5

-5

-10 (0, -8) Full file at https://TestbankDirect.eu/

Trang 53

-5

-10

(-6, 4) (-2, 4)(-2, 2)

(6, 6)

(6, 2.4) (13, 3.6)

x

y 10

5

-5

-10

(-6, 4) (-2, 4)(-2, 2)

(6, 6)

(6, 2.4) (13, 3.6)

-5

(-4, 2)

(3, 3)

A)f(x) = - 1

2x if -4 ≤ x ≤ 0

x if 0 < x ≤ 3

B)f(x) =

1

2x if -4 < x < 0

x if 0 < x < 3C)

f(x) = - 1

2x if -4 < x < 0

x if 0 < x < 3

D)f(x) = -2x if -4 ≤ x ≤ 0

x if 0 < x ≤ 3

Trang 54

x

y 5

-5

(0, 1)

(3, 4)

(3, 2) (5, 3)

x

y 5

-5

(0, 1)

(3, 4)

(3, 2) (5, 3)

A)f(x) =

x + 1 if 0 ≤ x ≤ 31

2x +

1

2 if 3 < x ≤ 5

B)f(x) =

x + 1 if 0 ≤ x ≤ 31

2x if 3 < x ≤ 5C)

f(x) =

x + 1 if 0 ≤ x ≤ 31

2x + 2 if 3 < x ≤ 5

D)f(x) =

x + 1 if 0 ≤ x ≤ 31

2x -

1

2 if 3 < x ≤ 514)

x

y 5

2x if 0 < x ≤ 3

Trang 55

x

y 5

2x if x > 0C)

f(x) =

3

4x + 4 if -3 ≤ x ≤ 03

1st 25 therms $0.6686/thermOver 25 therms $0.85870/thermWhat is the charge for using 25 therms in one month?

What is the charge for using 45 therms in one month?

Construct a function that gives the monthly charge C for x therms of gas

Trang 56

18) An electric company has the following rate schedule for electricity usage in single -family residences:

Monthly service charge $4.93Per kilowatt service charge

1st 300 kilowatts $0.11589/kWOver 300 kilowatts $0.13321/kWWhat is the charge for using 300 kilowatts in one month?

What is the charge for 75 hours of high-speed Internet use in one month?

What is the charge for 135 hours of high-speed Internet use in one month?

20) The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce

the same heat loss as the given temperature and wind speed. One formula for computing the equivalenttemperature is

21) A cellular phone plan had the following schedule of charges:

Basic service, including 100 minutes of calls $20.00 per month2nd 100 minutes of calls $0.075 per minuteAdditional minutes of calls $0.10 per minute

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Test bank for precalculus concepts through functions a right triangle approach to trigonometry 3rd edition by sullivan

Building Mathematical Models Using Variation