Deck 11: Functions and Relations

Question 1

Find the zeros of the function:

A)
B)
C)
D)
E)

Answer 1

Question 2

Use the discriminant to determine the number of x-intercepts of the graph:

A) None
B) Two
C) One

Answer 2

Two

Question 3

Use the discriminant to determine the number of x-intercepts of the graph:

A) None
B) Two
C) One

Answer 3

None

Question 4

Find the x-intercepts of the parabola:

A) (0,-3),
B) (0,-3),
C) (-3,0),
D) (3,0),
E) No x-intercepts

Question 5

Find the x-intercepts of the parabola:

A) (0,8),
B) (0,8),
C) (-8,0),
D) (8,0),
E) No x-intercepts

Question 6

Find the vertex and axis of symmetry, and then graph the parabola given by:

A) Vertex: ( ); Axis of symmetry: x =
B) Vertex: ( ); Axis of symmetry: x =
C) Vertex: ( ) ; Axis of symmetry: x =

Question 7

State the domain and range of the function:

A) Domain:
Range:
B) Domain:
Range:
C) Domain:
Range:
D) Domain:
Range:
E) Domain:
Range:

Question 8

State the domain and range of the function:

A) Domain:
Range:
B) Domain:
Range:
C) Domain:
Range:
D) Domain:
Range:
E) Domain:
Range:

Question 9

Find the x-intercepts of the parabola:

A) (3,0)
B) (3,0), (-2,0)
C) (0,-3), (3,0)
D) (0,-3), (0,3)
E) (-3,0), (3,0)

Question 10

Find the vertex and axis of symmetry, and then graph the parabola given by:

A) Vertex: (2, -1); Axis of symmetry: x = 2
B) Vertex: (2, -1); Axis of symmetry: x = 2
C) Vertex: (1, -1); Axis of symmetry: x = 1

Question 11

Find the zeros of the function:

A) -4, -8
B) ,
C) ,
D) -4, 8
E) ,

Question 12

Find the x-intercepts of the parabola:

A) (0,-1), (0,3)
B) (0,-1), (3, 0)
C) (1,0), (3,0)
D) (1, 3)
E) (-1,0), (3, 0)

Question 13

Find the vertex and axis of symmetry, and then graph the parabola given by:

A) Vertex: (2, -1); Axis of symmetry: x = 2
B) Vertex: (-2, -8); Axis of symmetry: x = -2
C) Vertex: (1, -2); Axis of symmetry: x = 1

Question 14

Find the zeros of the function:

A) 0, 3
B)
C)
D) 0, 2
E)

Question 15

Find the zeros of the function:

A) 4, 0
B) -4, 0
C) -4, 8
D) -4, -8
E) 4, 8

Question 16

Find the zeros of the function:

A)
B)
C)
D) 0, 3
E) 0, 2

Question 17

Find the zeros of the function:

A)
B)
C)
D)
E) 0, 8

Question 18

Use the discriminant to determine the number of x-intercepts of the graph:

A) One
B) Two
C) None

Question 19

Find the x-intercepts of the parabola:

A) No x-intercepts
B) (-4,0),
C) (0,-4),
D) (0,-4),
E) (4,0),

Question 20

Find the x-intercepts of the parabola:

A) (-2,0),
B) (0,-2),
C)
D) (0,-2),
E) (2,0),

Question 21

Given the graph of . Use translations to draw the graphs .

A)
B)
C)
D)
E)

Question 22

Find the minimum or maximum of the quadratic function:

A) Minimum: 5
B) Maximum: -3
C) Minimum: 1
D) Minimum: 11
E) Minimum: 3

Question 23

The height, s, in feet, of a rock thrown upward at an initial speed of 76 ft/s from a cliff 40 ft above the ocean beach is given by the function where t is the time in seconds. Find the maximum height above the beach that the rock will attain.

A) 2.4 ft
B) 122.25 ft
C) 130.25 ft
D) 134.25 ft
E) 130 ft

Question 24

Use the discriminant to determine the number of x-intercepts of the graph:

A) One
B) Two
C) None

Question 25

Find the minimum or maximum of the quadratic function:

A) Minimum: -5
B) Minimum: 10
C) Minimum: -10
D) Maximum: -2
E) Maximum: 8

Question 26

Find two numbers whose difference is 46 and whose product is a minimum.

A) 23, -23
B) -23, -69
C) -25, -71
D) 33, -13
E) 26, -20

Question 27

Find the minimum or maximum of the quadratic function:

A) Minimum: 3.5
B) Minimum: 0.25
C) Minimum: -0.25
D) Minimum: 2.5
E) Minimum: -3.5

Question 28

A tour operator believes the profit P, in dollars, from selling x tickets is given by Using this model, what is the maximum profit the tour operator can expect?

A) $6912
B) $96
C) $2304
D) $2303
E) $2300

Question 29

A manufacturer of microwave ovens believes that the revenue R, in dollars, the company receives is related to the price P, in dollars, of an oven by the function What price will give the maximum revenue?

A) $15,125
B) $266
C) $270
D) $550
E) $275

Question 30

Given the graph of . Use reflections to draw the graphs .

A)
B)
C)
D)
E)

Question 31

Find the minimum or maximum of the quadratic function:

A) Maximum: 18
B) Maximum: -6
C) Minimum: -14
D) Minimum: 4
E) Minimum: 14

Question 32

Let Find:

A) -11
B) -5
C)
D)
E)

Question 33

Given the graph of called a sawtooth wave. Use translations to draw the graphs .

A)
B)
C)
D)
E)

Question 34

Let Find:

A) 72
B) 1232
C) -164
D) -260
E) 2348

Question 35

Find the minimum or maximum of the quadratic function:

A) Minimum: -1
B) Minimum: 5
C) Minimum: 4
D) Minimum: -4
E) Minimum: 12

Question 36

Let Find:

A) -64
B) -70
C) -52
D) -76
E) -32

Question 37

Given the graph of . Use translations to draw the graphs .

A)
B)
C)
D)
E)

Question 38

Given the graph of . Use translations to draw the graphs .

A)
B)
C)
D)
E)

Question 39

Find two numbers whose sum is 38 and whose product is a maximum.

A) 30; 8
B) 19; 19
C) 22; 16
D) 13; 25
E) 23; 15

Question 40

Use the discriminant to determine the number of x-intercepts of the graph:

A) None
B) Two
C) One

Question 41

Let Find:

A) 22
B) 10
C) -2
D) -7
E) -1

Question 42

Let Find

A)
B)
C)
D)
E)

Question 43

Let Find:

A) 3
B) -1
C) -4
D) -3
E) -2

Question 44

Determine whether the function given below has an inverse.

A) Inverse exists
B) No inverse

Question 45

Use the Composition of Inverse Function Property to determine whether the functions given below are inverses.

A) No
B) Yes

Question 46

Find .

A)
B) No inverse
C)
D)
E)

Question 47

Suppose the spread of an oil leak from a tanker can be approximated by a circle with the tanker at its center and radius r, in feet. The radius of the spill t hours after the beginning of the leak is given by Find the area of the spill as a function of time.

A)
B)
C)
D)
E)

Question 48

Suppose the spread of an oil leak from a tanker can be approximated by a circle with the tanker at its center and radius r, in feet. The radius of the spill t hours after the beginning of the leak is given by Find the area of the spill after 3 h. Round to the nearest whole number.

A) 38,708 ft²
B) 38,785 ft²
C) 12,321 ft²
D) 1046 ft²
E) 697 ft²

Question 49

Find

A)
B)
C)
D) No inverse
E)

Question 50

Find .

A)
B)
C) No inverse
D)
E)

Question 51

Determine whether the graph shown below is the graph of a 1-1 function.

A) Yes
B) No

Question 52

Find .

A)
B)
C)
D) No inverse
E)

Question 53

Let Find:

A) -69
B) -70
C) -65
D) -61
E) -25

Question 54

Let Find:

A) -12
B) -2
C) -42
D) -26
E) 28

Question 55

Use the Composition of Inverse Function Property to determine whether the functions given below are inverses.

A) Yes
B) No

Question 56

Determine whether the graph shown below is the graph of a 1-1 function.

A) Yes
B) No

Question 57

Let Find:

A) 56
B) 191
C) 193
D) 156
E) 183

Question 58

Let Find

A)
B)
C)
D)
E)

Question 59

Let Find

A)
B)
C)
D)
E)

Question 60

Determine whether the function given below has an inverse.

A) No Inverse
B) Inverse exists

Question 61

Use the Composition of Inverse Function Property to determine whether the functions given below are inverses.

A) No
B) Yes

Question 62

Use the Composition of Inverse Function Property to determine whether the functions given below are inverses.

A) Yes
B) No