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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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Which statement explains why the value of is 2 but the value of is –3?

Question illustration
A
because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4
B
because 2.4 rounds to 2, and –2.4 rounds to –3
C
because 2.4 is positive, and –2.4 is negative
D
because 2 is the least integer greater than 2.4, and –3 is the least integer greater than –2.4
3

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
4

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
5

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)
6

What is the value of ?

Question illustration
A
–13
B
–12
C
12
D
13
7

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.
8

What is the value of ?

Question illustration
A
–36
B
–33
C
–32
D
–30
9

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
10

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.

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