AnswersVA-Mathematical AnalysisStep Functions

Step Functions Answers

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A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound. Which equation represents the cost, in dollars, of shipping a package that weighs x pounds?

A
, where x > 0
Option A
B
, where x > 0
Option B
C
, where x > 0
Option C
D
, where x > 0
Option D
2
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What is the value of ?

Question illustration
A
–36
B
–33
C
–32
D
–30
3

Jeremiah lives in New York City and takes a taxi almost everywhere he goes. In order to calculate the price of his taxi ride, Jeremiah came up with the equation P = 1.80 + 2.50, where x is the number of miles or partial miles traveled in the taxi.Explain the meaning of the constant 2.50 as it relates to the situation.

Question illustration
A
$2.50 is the base amount that Jeremiah must pay in order for the taxi to pick him up before he has been driven anywhere.
B
$2.50 is the amount Jeremiah must pay as long as the taxi has not driven a complete mile.
C
For every mile or partial mile the taxi drives, Jeremiah must pay an additional $2.50.
D
Jeremiah must pay $2.50 plus $1.80, or $4.30, per mile for each taxi ride.
4

For which x-values is the graph below discontinuous?

Question illustration
A
{...–3, –2, –1, 0, 1, 2, 3, ...}
B
{... –3, –1, 1, 3, ...}
C
{...–4, –2, 0, 2, 4, ...}
D
{...–3, –1, 0, 1, 3, ...}
5

What are the domain and range of the step function with the equation below?

Question illustration
A
The domain is all real numbers, and the range is all real numbers.
B
The domain is all integers, and the range is all integers that are multiples of 3.
C
The domain is all real numbers, and the range is all integers that are multiples of 3.
D
The domain is all integers, and the range is all real numbers.
6

Where is the graph of discontinuous?

Question illustration
A
all real numbers
B
all integers
C
only at multiples of 3
D
only at multiples of 4
7

Kareem wrote the expressions shown below.Which pair is equivalent?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
8

What is the value of ?

Question illustration
A
3
B
3.5
C
3.6
D
4

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