NC.M1.F-IF.5 Function Intervals

• all real numbers

An ice rink can hold up to 400 skaters. The owners charge $200 to rent the rink for 6 hours, plus $4 for each person skating. The total cost to rent the rink is a function of the number of people skating, p. Which inequality best represents the domain of the function?

• all real numbers

This graph shows the percent of households worldwide that had a computer, y, x years after 2005.

What is the range of this data?

Keylee owns a cabin that she rents to people for a maximum of 21 nights. She uses the function f(x) = 175x + 50 to calculate the rental cost for x nights. What is the domain for the function in this context?

• 0 ≤ x ≤ 3,725, where x is an integer

• 0 < x < 3,725, where x is an integer

• 0 ≤ x ≤ 21, where x is an integer

• 0 < x < 21, where x is an integer

Alexa is starting a new exercise program.

Each day of the first week she will exercise 30 minutes.

Each week thereafter, she will increase her daily exercise time by 5 minutes until she is able to exercise for 60 minutes each day.

A function represents the number of minutes she will exercise in the nth week.

What is the domain of the function?

• {0, 1, 2, 3, 4, 5, 6, 7}

• {1, 2, 3, 4, 5, 6, 7}

• {25, 30, 35, 40, 45, 50, 55, 60}

• {30, 35, 40, 45, 50, 55, 60}

A 150-gallon water tank is 50% filled with water. It begins leaking at a rate of 4 gallons per hour, x. The amount of water in the tank, y, is a function of time. What is the domain of the function?

• 0 ≤ x ≤ 18.75

• 0 ≤ y ≤ 18.75

• 0 ≤ x ≤ 75

• 0 ≤ y ≤ 75

Nephi’s Plumbing charges a $75 diagnostic fee and $60 per hour for repairs. Sterling has a repair that could take up to 10 hours to complete. The amount of money, f(x), the company charges Sterling is a function of the number of hours, x, the job takes. What is the best range of the function?

• 75 ≤ x ≤ 675

• 75 ≤ f(x) ≤ 675

• 0 ≤ x ≤ 10

• 0 ≤ f(x) ≤ 10

Asher mows yards to earn money on weekends.

He charges $25 for each yard he mows.

He has time to mow, at most, 6 yards per weekend.

The function P(x) represents the money Asher earns for mowing x yards on a weekend.

What is the domain of this function?

• 0 ≤ x ≤ 6, where x is an integer

• 0 ≤ x ≤ 25, where x is an integer

• 0 ≤ x ≤ 150, where x is an integer

• 6 ≤ x ≤ 25, where x is an integer

The function f(x) = 2.5x models the amount of water, in quarts, in a bucket after x seconds. Ben needs to fill a 55-quart bucket. Which is the most appropriate domain for the function?

• x ≥ 0

• x ≤ 22

• 0 ≤ x ≤ 22

• 0 ≤ x ≤ 55