Answers Common Core Algebra II - MA3111 B-ICAbsolute Value Functions

Step Functions Answers

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

all integer values of x

all real number values of x

only negative values of x

only noninteger values of x

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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.

$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.

$2.50 is the amount Jeremiah must pay as long as the taxi has not driven a complete mile.

For every mile or partial mile the taxi drives, Jeremiah must pay an additional $2.50.

Jeremiah must pay $2.50 plus $1.80, or $4.30, per mile for each taxi ride.

What is the value of ?

–36

–33

–32

–30

For which x-values is the graph below discontinuous?

{...–3, –2, –1, 0, 1, 2, 3, ...}

{... –3, –1, 1, 3, ...}

{...–4, –2, 0, 2, 4, ...}

{...–3, –1, 0, 1, 3, ...}

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

because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4

because 2.4 rounds to 2, and –2.4 rounds to –3

because 2.4 is positive, and –2.4 is negative

because 2 is the least integer greater than 2.4, and –3 is the least integer greater than –2.4

What is the value of ?

–2

–1

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?

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

The steps are at y = –2 for , at y = –1 for , and at y = 0 for .

The steps are at y = 0 for , at y = 1 for , and at y = 2 for .

The steps are at y = 1 for , at y = 2 for , and at y = 3 for .

The steps are at y = –3 for , at y = –2 for , and at y = –1 for .

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

and

What is the value of ?

3.5

3.6

What is the value of ?

–5

–4.6

–4.5

–4

A skate shop rents roller skates as shown in the table below. Roller Skate RentalsTimeCostup to 60 minutes$5up to 2 hours$10up to 5 hours$20daily$25Which graph and function model this situation, where c is the cost, in dollars, of renting skates, and t is the number of hours in a single day that the skates are rented?

Option

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

The domain is all real numbers, and the range is all real numbers.

The domain is all integers, and the range is all integers that are multiples of 3.

The domain is all real numbers, and the range is all integers that are multiples of 3.

The domain is all integers, and the range is all real numbers.

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?

, where x > 0