Step Functions Answers

1

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Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function.What is the value of y when x=5.7?

A

5

B

5.50

C

5.75

D

6

2

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The graph represents y = ⌈x⌉ + 1.

A

–5

B

–4

C

–2

D

–1

3

A step function h(x) is represented by y = –2⌊x⌋. Which phrase best describes the range of the function h(x)?

A

all real numbers

B

all rational numbers

C

all negative integers

D

all even integers

4

The graph represents the parking fees at a mall parking lot.

A

Parking costs $1 per hour for the entire day.

B

Parking costs $2 per hour for the entire day.

C

The total cost of 2 hours of parking is $1.

D

The total cost of 1 hour of parking is $2.

5

Which is the graph of the step function f(x)?f(x) =

A

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).

B

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to the right at y = 1.

C

On a coordinate plane, a piecewise function has 3 lines. The first line has a closed circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has a closed circle at (1, 1) and continues horizontally to the right at y = 1.

D

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).

6

The step function f(x) is graphed.

A

-2

B

-1

C

0

D

1

7

What is the domain of the step function f(x) = ⌈2x⌉ – 1?

A

{x| x ≥ –1}

B

{x| x ≥ 1}

C

{x| x is an integer}

D

{x| x is a real number}

8

Which is the graph of g(x) = ⌈x + 3⌉?

A

Option

B

Option

C

Option

D

Option

9

An office supply store offers banner printing services. The store charges $4 to print each one-foot-long section of a banner that is three feet tall. Which graph represents the cost to print a three-foot-tall banner that is x feet long?

A

Option

B

Option

C

Option

D

Option

10

The cost of a single ticket depends on the number of tickets, t, purchased in a group, as represented by the function C(t).C(t) = What is the total cost for 20 tickets?

A

$14.50

B

$16.00

C

$290.00

D

$320.00

11

A clothing store uses the step function f(x) to recommend jeans sizes as a function of x, a child’s height in inches.f(x) = According to the function, which is the height of a child who should wear size 2 jeans?

A

41.9 inches

B

42 inches

C

44 inches

D

44.1 inches

12

The graph represents the parking fees at a mall parking lot.

A

Parking costs $1 per hour for the entire day.

B

Parking costs $2 per hour for the entire day.

C

The total cost of 2 hours of parking is $1.

D

The total cost of 1 hour of parking is $2.

13

The graph represents f(x) = .

A

-2

B

0

C

1

D

2

14

A step function h(x) is represented by y = –2⌊x⌋. Which phrase best describes the range of the function h(x)?

A

all real numbers

B

all rational numbers

C

all negative integers

D

all even integers

15

Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function.What is the value of y when x=5.7?

A

5

B

5.50

C

5.75

D

6

16

What is the domain of the step function f(x) = ⌈2x⌉ – 1?

A

{x| x ≥ –1}

B

{x| x ≥ 1}

C

{x| x is an integer}

D

{x| x is a real number}

17

Which is the graph of y = ⌊x⌋ – 2?

A

Option

B

Option

C

Option

D

Option

18

The step function f(x) is graphed.

A

-3

B

-1

C

0

D

1

19

Which is the graph of g(x) = ⌈x + 3⌉?

A

Option

B

Option

C

Option

D

Option

20

Which is the graph of the step function f(x)?f(x) =

A

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).

B

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has a closed circle at (negative 1, 0) and continues horizontally to a closed circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to the right at y = 1.

C

On a coordinate plane, a piecewise function has 3 lines. The first line has a closed circle at (negative 1, negative 1) and continues horizontally to the left at y = negative 1. The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has a closed circle at (1, 1) and continues horizontally to the right at y = 1.

D

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 3, negative 1) and continues horizontally to an open circle at (negative 1, negative 1). The second line has an open circle at (negative 1, 0) and continues horizontally to an open circle at (1, 0). The third line has an open circle at (1, 1) and continues horizontally to an open circle at (3, 1).

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