AnswersVA-Mathematical AnalysisStep Functions

Step Functions Answers

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The United States Postal Service charges $0.55 to mail a first-class letter that weighs up to 1 ounce. Each additional ounce costs $0.15. Which equation represents the situation?

A
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Option A
B
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Option B
C
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Option C
D
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Option D
2
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In the function , which values of the function are equivalent?

Question illustration
A
f(–1) and f(–2)
B
f(1) and f(0)
C
f(–3) and f(–2.1)
D
f(2) and f(1.9)
3

Which set of numbers best describes the possible values of x in the equation below?

Question illustration
A
all integer values of x
B
all real number values of x
C
only negative values of x
D
only noninteger values of x
4

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
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

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.
7

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, ...}
8

The cost of sending an overnight package from Kansas City to Miami is $23.50 for a package weighing up to but not including 1 pound, and $3.80 for each additional pound or portion of a pound. A model for the total cost C (in dollars) of sending the package is C = 23.50 + 3.80, x > 0, where x is the weight (in pounds). What is the meaning of the coefficient 3.80 in the context of the problem?

Question illustration
A
When the package weighs less than one pound, the price of the package is $3.80.
B
For every pound that the package weight increases, the price of sending it increases by $3.80.
C
For every pound that the package weight increases, the price of sending it increases by $23.50.
D
When the package weighs less than one pound, the price of the package is $23.50.
9

What is the value of ?

Question illustration
A
3
B
3.5
C
3.6
D
4
10

Which statement describes the graph of on [0, 3)?

Question illustration
A
The steps are at y = –2 for , at y = –1 for , and at y = 0 for .
Option A
B
The steps are at y = 0 for , at y = 1 for , and at y = 2 for .
Option B
C
The steps are at y = 1 for , at y = 2 for , and at y = 3 for .
Option C
D
The steps are at y = –3 for , at y = –2 for , and at y = –1 for .
Option D
15

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
21

Used books cost $2.25 each. Which expression represents the total number of books that can be purchased for $10?

A
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Option A
B
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Option B
C
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Option C
D
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Option D

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