Deck 1: Functions

Question 1

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Answer 1

Function

Question 2

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Answer 2

Function

Question 3

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Answer 3

Not a function

Question 4

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Question 5

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Question 6

Determine whether or not the graph is a graph of a function of x.

-

A) Function
B) Not a function

Question 7

Find the domain and graph the function.

-f(x) = 3x - 6

A) D: (- $\infty$ , $\infty$ )

B) D: [0, $\infty$ )

C) D: (- $\infty$ , $\infty$ )

D) D: (- $\infty$ , $\infty$ )

Question 8

Find the domain and graph the function.

-g(x) = 2 + 2x - x²

A) D: (- $\infty$ , 3]

B) D: (- $\infty$ , $\infty$ )

C) D: (- $\infty$ , $\infty$ )

D) D: (- $\infty$ , $\infty$ )

Question 9

Find the domain and graph the function.

-F(x) =

A) D: (- $\infty$ , $\infty$ )

B) D: [0, $\infty$ )

C) D: (- $\infty$ , 0]


D)D: (- $\infty$ , 0)

Question 10

Find the domain and graph the function.

-G(x) =

A) D: (- $\infty$ , $\infty$ )

B)D: (- $\infty$ , 0]

C) D: [0, $\infty$ )

D)D: (- $\infty$ , 0)

Question 11

Find the domain and graph the function.

-F(t) = .

A)D: (- $\infty$ , 0) (0, $\infty$ )

B) D: (- $\infty$ , 1) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 ( 1>, $\infty$ )

C)
D: (- $\infty$ , 1) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 ( 1, $\infty$ )

D) D: (- $\infty$ , $\infty$ )

Question 12

Find the domain and graph the function.

-G(t) =

A) D: (- $\infty$ , -3) ( -3, $\infty$ )

B) D: (- $\infty$ , $\infty$ )


C) D: (- $\infty$ , -3)11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 ( -3, $\infty$ )



D) D: (- $\infty$ , 0) 11ee7b09_453f_4329_ae82_2b7669cf7fd7_TB9661_11 (0, $\infty$ )

Question 13

Find the domain and range of the function.

-f(x) = 4 -

A) D: (- $\infty$ , 4], R: (- $\infty$ , $\infty$ )
B)D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , $\infty$ )
C) D: (- $\infty$ , $\infty$ ), R: [ 4, $\infty$ )
D) D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , 4]

Question 14

Find the domain and range of the function.

-F(t) = + 5

A)D: [ -25, $\infty$ ), R: [ 5, $\infty$ )
B) D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , $\infty$ )
C) D: (- $\infty$ , $\infty$ ), R: [ 5, $\infty$ )
D)D: [0, $\infty$ ), R: (- $\infty$ , 5]

Question 15

Find the domain and range of the function.

-g(z) = -5 -

A) D: (- $\infty$ ,0], R: [ -5, $\infty$ )
B)D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , -5]
C) D: (- $\infty$ -5], R: (- $\infty$ , $\infty$ )
D)D: [0, $\infty$ ), R: (- $\infty$ , -5]

Question 16

Find the domain and range of the function.

-f(x) = 7 +

A) D: (- $\infty$ ,0], R: (- $\infty$ , 7]
B) D: (- $\infty$ , $\infty$ ), R: [ 7, $\infty$ )
C) D: [0, $\infty$ ), R: (- $\infty$ , $\infty$ )
D) D: [0, $\infty$ ), R: [ 7, $\infty$ )

Question 17

Find the domain and range of the function.

-F(t) =

A) D: [0, $\infty$ ), R: (- $\infty$ , $\infty$ )
B) D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , $\infty$ )
C) D: (0, $\infty$ ), R: (0, $\infty$ )
D) D: (- $\infty$ ,0), R: (- $\infty$ ,0)

Question 18

Find the domain and range of the function.

-g(z) =

A) D: [1, $\infty$ ), R: (- $\infty$ , $\infty$ )
B) D: [0, $\infty$ ), R: (- $\infty$ , $\infty$ )
C) D: (-1, $\infty$ ), R: (- $\infty$ ,0)
D) D: (- $\infty$ ,-1), R: (0, $\infty$ )

Question 19

Find the domain and range of the function.

-f(x) =

A) D: (- $\infty$ , $\infty$ ), R:
B) D: (- $\infty$ ,0], R:(- $\infty$ ,0]
C) D: [0, $\infty$ ), R: (- $\infty$ , $\infty$ )
D)D: [0, $\infty$ ), R:

Question 20

Find the domain and range of the function.

-F(t) =

A)D: (- $\infty$ , $\infty$ ), R: (- $\infty$ , $\infty$ )
B) D: (0, $\infty$ ), R: (0, $\infty$ )
C) D: [0, $\infty$ ), R: [0, $\infty$ )
D) D: (- $\infty$ ,0), R: (- $\infty$ ,0)

Question 21

Find the domain and range of the function.

-g(z) =

A) D: (- $\infty$ , $\infty$ ), R: (0, 5)
B) D: [0, $\infty$ ), R: (- $\infty$ , $\infty$ )
C) D: (-5, 5), R: (-5, 5)
D)D: [-5, 5], R: [0, 5]

Question 22

Determine an appropriate domain of the function. Identify the independent and dependent variables.

-A cylindrical water tank with a radius of 9 feet and a height of 65 feet is filled to a height of h. The volume V of water (in cubic feet) is given by the function g(h) = 81 $\pi$ h.

A)D = [0, 65]The independent variable is h.The dependent variable is V.
B) D = [0, 65] The independent variable is V.The dependent variable is h.
C) D = [0, 5265 $\pi$ ] The independent variable is V.The dependent variable is h.
D) D = [0, 81]The independent variable is h.The dependent variable is V.

Question 23

Determine an appropriate domain of the function. Identify the independent and dependent variables.

-A weather balloon of radius r (in meters) is filled with air. The volume V of the balloon is given by the function . Assume the balloon can hold up to 4 of air.

A) D = The independent variable is V.The dependent variable is r.
B)D = The independent variable is r.The dependent variable is V.
C)D = The independent variable is r.The dependent variable is V.
D) D = [0, 4]The independent variable is r.The dependent variable is V.

Question 24

Solve the problem.

-If f(x) = 5x + 7 and g(x) = 2x - 1, find f(g(x)).

A)10x + 13
B)10x + 2
C) 10x + 6
D) 10x + 12

Question 25

Solve the problem.

-If f(x) = -5x + 9 and g(x) = 4x + 8, find g(f(x)).

A) -20x + 44
B)20x + 44
C)-20x - 28
D)-20x + 49

Question 26

Solve the problem.

-If f(x) = and g(x) = 7x + 4, find g(f(x)).

A) 7x + 24
B)-
C) x + 8
D)x

Question 27

Solve the problem.

-If f(x) = and g(x) = 8x - 12, find f(g(x)).

A) 8
B)2
C) 8 - 12
D) 2

Question 28

Solve the problem.

-If f(x) = 4x² + 2x + 7 and g(x) = 2x - 8, find g(f(x)).

A) 8x² + 4x + 22
B) 8x² + 4x + 6
C) 4x² + 4x + 6
D) 4x² + 2x - 1

Question 29

Solve the problem.

-If f(x) = and g(x) = 3x⁵, find g(f(x)).

A)
B)

C)
D)

Question 30

Solve the problem.

-If f(x) = -3x + 8 and g(x) = -5x² + 3x - 8, find g(f(-5)).

A) -2584
B) 2
C) 452
D) -54

Question 31

Solve the problem.

-If f(x) = -5x + 8 and g(x) = 6x² - 5x + 5, find g(f( 8)).

A) -1737
B) 6309
C) -57
D) -27

Question 32

Solve the problem.

-If f(x) = , g(x) = , and h(x) = 3x+ 9, find f(g(h(x))).

A) +3
B)
C) 3 + 9
D)

Question 33

Solve the problem.

-If f(x) = , g(x) = , and h(x) = 5x+ 20, find h(g(f(x))).

A) +4
B) +20
C)
D) 5 + 20

Question 34

Express the given function as a composite of functions f and g such that y = f(g(x)).

-y =

A)

B)

C)

D)

Question 35

Express the given function as a composite of functions f and g such that y = f(g(x)).

-y =

A)

B)

C)

D)

Question 36

Express the given function as a composite of functions f and g such that y = f(g(x)).

-y = + 6

A)

B)

C)

D)

Question 37

Express the given function as a composite of functions f and g such that y = f(g(x)).

-y =

A)

B)

C)

D)

Question 38

Express the given function as a composite of functions f and g such that y = f(g(x)).

-y =

A)

B)

C)

D)

Question 39

Solve the problem.

-Let f(x) = . Find a function y = g(x) so that (f g)(x) = x.

A) g(x) = x(x - 6)
B)g(x) =
C) g(x) =
D) g(x) =

Question 40

Solve the problem.

-Let f(x) = . Find a function y = g(x) so that (f g)(x) = .

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

Question 41

Solve the problem.

-Let g(x) = . Find a function y = f(x) so that (f g)(x) = .

A) f(x) =
B)f(x) = x
C) f(x) =
D) f(x) =

Question 42

Solve the problem.

-Let g(x) = x + 2. Find a function y = f(x) so that (f g)(x) = 4x + 8

A) f(x) = 4(x + 1)
B) f(x) = 4x + 2
C) f(x) = 4x
D) f(x) = 4x - 2

Question 43

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) = 7x + 1

A) 7h; 7a
B) 7; 7
C)7x - 7h; 7x - 7a
D) 7; 7x - 7a

Question 44

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) =

A)

B)

C)

D)

Question 45

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) = 6

A)

B)

C)

D)

Question 46

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) = 2 + 7x - 5

A) 4x + 2h + 7; 2x + 2a + 7
B) 4x + 4h + 7; 2x - 2a - 7
C) 4 + h; 4x + 4a + 7
D)4x + 7h - 5; 4x + 4a + 7

Question 47

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) =

A)

B)

C)

D)

Question 48

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) =

A)
B)
C)
D)

Question 49

Simplify the difference quotients and for the following function. Rationalize the numerator when necessary.

-f(x) = -

A)

B)
C)

D)

Question 50

Graph the function. Determine the symmetry, if any, of the function.

-y =

A) Symmetric about the origin

B) No symmetry

C) Symmetric about the y-axis

D)Symmetric about the origin

Question 51

Graph the function. Determine the symmetry, if any, of the function.

-y = -

A) Symmetric about the y-axis

B) No symmetry

C) Symmetric about the y-axis

D) Symmetric about the y-axis

Question 52

Graph the function. Determine the symmetry, if any, of the function.

-y =

A) No symmetry

B) Symmetric about the origin

C) Symmetric about the origin

D)Symmetric about the origin

Question 53

Graph the function. Determine the symmetry, if any, of the function.

-y = -|x|

A) Symmetric about the origin

B) Symmetric about the y-axis

C) Symmetric about the y-axis

D)Symmetric about the x-axis

Question 54

Graph the function. Determine the symmetry, if any, of the function.

-y =

A) Symmetric about the y-axis

B) Symmetric about the y-axis

C) No symmetry

D) No symmetry

Question 55

Graph the function. Determine the symmetry, if any, of the function.

-y = 3

A)Symmetric about the x-axis

B) No symmetry

C) Symmetric about the x-axis

D) No symmetry

Question 56

Graph the function. Determine the symmetry, if any, of the function.

-y =

A)No symmetry

B)No symmetry

C) Symmetric about the y-axis

D) Symmetric about the y-axis

Question 57

Graph the function. Determine the symmetry, if any, of the function.

-y =

A) No symmetry

B)Symmetric about the y-axis

C) No symmetry

D)Symmetric about the y-axis

Question 58

Solve the problem.

-The distance an object is from the ground after being tossed from a hot air balloon 770 feet in the air is a function of time: f(t) where f(t) is height and t is the amount of time the object has been in the air. Predict the height of the object after 5.5 seconds.

A) 252.73 feet
B) 313.23 feet
C) 711.70 feet
D)0 feet

Question 59

Solve the problem.

-A marine biologist determines that the size, p, of a population of crabs, after t days can be modeled by the function .Assuming that this model continues to be accurate, when will this population become extinct? (Round to the nearest day.)

A) 911 days
B) 547 days
C) 707 days
D) 1512 days

Question 60

Solve the problem.

-The wind speed is tracked as a storm approaches. The maximum speed w of wind gusts, in miles per hour, t hours after midnight on the night of an approaching storm is given in the figure.
a.Find the slope of the secant line that passes through points (1, 17.2) and (3, 26.9). Interpret your answer as an average rate of change over the interval 1 $\le$ t $\le$ 3.
b.Repeat the procedure outlined in part (a) for the secant line that passes through points (7, 34.4) and c. Notice that the curve in the figure is generally increasing until t = 6, and is generally decreasing after
Give a plausible explanation for this behavior.

A)
a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph
c.The storm reached its farthest point about 6:00 a.m. and is moving closer after that.
B)
a. 9.7, the wind is increasing in speed at an average rate of 9.7 mph per hour
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph per hour
c.The storm reached its closest point about 6:00 a.m. and is moving away after that.
C)
a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph
c. The storm reached its closest point about 6:00 a.m. and is moving away after that.
D)
a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph per hour
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph per hour
c.The storm reached its closest point about 6:00 a.m. and is moving away after that.

Question 61

Solve the problem.

-The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.

A) y =
B) y = x² - 6
C) y = x² + 6
D) y =

Question 62

Solve the problem.

-The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.

A) y =
B) y = x² - 2
C) y =
D) y = x² + 2

Question 63

Solve the problem.

-The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.

A) y = x² - 5
B) y =
C) y = x² + 5
D)y =

Question 64

Solve the problem.

-The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.

A)y =
B) y = x² + 6
C) y =
D) y = x² - 6

Question 65

Solve the problem.

-The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.

A) y = -x² - 4
B) y = -
C) y = -x² + 4
D) y = -

Question 66

Solve the problem.

-The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.

A) y = -x² - 4
B) y = -
C) y = -x² + 4
D)y = -

Question 67

Solve the problem.

-The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.

A) y = -

B)y = -x² - 2
C) y = -
D) y = -x² + 2

Question 68

Solve the problem.

-The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.

A) y = -x² - 4
B) y = -
C)y = -
D) y = -x² + 4

Question 69

Solve the problem.

-The accompanying figure shows the graph of y = shifted to a new position. Write the equation for the new graph.

A)y = (x + 5)² - 3
B) y = (x - 3)² - 5
C) y = (x + 3)² - 5
D) y = (x - 3)² + 5

Question 70

Solve the problem.

-The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.

A) y = -(x + 2)² - 5
B) y = -(x + 5)² + 2
C) y = -(x + 5)² - 2
D) y = -(x - 5)² + 2

Question 71

Choose the graph that matches the function.

-f(x) = 3x + 4

A)

B)

C)

D)

Question 72

Choose the graph that matches the function.

-f(x) = 2x - 6

A)

B)

C)

D)

Question 73

Choose the graph that matches the function.

-f(x) = -4x + 3

A)

B)

C)

D)

Question 74

Choose the graph that matches the function.

-f(x) = -4x - 6

A)


B)

C)

D)

Question 75

Choose the graph that matches the function.

-f(x) = -2x

A)


B)


C)


D)

Question 76

Choose the graph that matches the function.

-f(x) = 3

A)


B)

C)

D)

Question 77

Choose the graph that matches the function.

-f(x) = x + 5

A)

B)

C)


D)

Question 78

Choose the graph that matches the function.

-f(x) = - x + 3

A)

B)

C)

D)

Question 79

Choose the graph that matches the function.

-f(x) = x - 6

A)

B)

C)


D)

Question 80

Choose the graph that matches the function.

-f(x) = - x - 4

A)

B)

C)

D)