Domain and range of linear functions: word problems

Paul works for a landscaping company during his school breaks. To prepare for a day of work, he fills his leaf blower with 2 gallons of fuel, which will last for 4 hours of use. The function V(h) represents the amount of fuel, in gallons, remaining in the leaf blower after h hours of use.

What is the domain of V(h)?

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Katie is driving from New York City to Boston. When she gets on the highway, she sets her car's cruise control to 60 miles per hour. She travels at that speed for 2 hours before exiting the highway. The function D(t) represents the distance Katie has traveled on the highway, t hours after she set her cruise control.

What is the domain of D(t)?

• 0 ≤ x ≤ 2

• x ≤ 2

• 0 ≤ x ≤ 120

• All real numbers

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The Astoria Park Community Pool sells season passes for $105 each. This season, they can sell up to 500 season passes. The function S(n) represents the amount of money the pool makes from selling n passes this season.

What is the domain of S(n)?

• all whole numbers

• all whole numbers less than or equal to 500

• all real numbers

• all real numbers less than or equal to 500

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Fred's cell phone plan charges $40 per month for unlimited talk, text, and data. In order to get this rate, he must pay in full on the first day of each month. The function C(m) represents the cost, in dollars, of m months of service.

What is the domain of C(m)?

• all whole numbers greater than or equal to 1

• all real numbers from 1 to 40

• all whole numbers less than or equal to 40

• all real numbers

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Quincy walks his dog each morning before school. They always walk the same 1-mile route, which takes 20 minutes. The function D(m) represents the distance Quincy and his dog have walked, in miles, after m minutes.

What is the domain of D(m)?

• all real numbers

• all whole numbers

• all whole numbers from 0 to 20

• all real numbers from 0 to 20

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Greta drives a tour bus in New York City. Her bus can seat up to 60 passengers. She collects a fee of $15 from each passenger, and always waits for at least 10 passengers to run the tour. The function C(p) represents the amount Greta collects, in dollars, for running a tour with p passengers.

What is the domain of C(p)?

• all whole numbers from 10 to 60

• all whole numbers

• all whole numbers from 0 to 10

• all whole numbers from 0 to 60

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TEKS.MATH.2A.2A

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Clayton teaches martial arts. He is planning to lead a self-defense seminar at his local community center. Students can sign up in advance for a price of $8. Clayton will run the seminar as long as at least 10 students sign up. He will close registration at 100 students due to space restrictions at the community center. The function C(t) represents the amount of money Clayton will earn, in dollars, for teaching the seminar to t students.

What is the domain of C(t)?

• all real numbers greater than or equal to 8

• all whole numbers from 10 to 100

• all whole numbers less than or equal to 10

• all real numbers from 8 to 100

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TEKS.MATH.2A.6K

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Today, Madelyn is running a 10-mile race and using her watch to help with pacing. She will run at a steady pace of 9 minutes per mile, and so she expects to finish the race in 90 minutes. The function D(m) represents the distance Madelyn has left to run, in miles, after m minutes.

What is the domain of D(m)?

• all whole numbers from 0 to 10

• all real numbers from 0 to 10

• all real numbers from 0 to 90

• all whole numbers from 0 to 90

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Park County Paddlers offers a daily kayaking tour of the Colorado River. They charge each visitor $40 to go on the tour, and they have enough equipment to take up to 12 visitors. The function C(v) represents the amount of money that Park County Paddlers will make in a day for taking v visitors on tour.

What is the domain of C(v)?

• all whole numbers less than or equal to 12

• all whole numbers greater than or equal to 12

• all real numbers less than or equal to 12

• all whole numbers

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TEKS.MATH.2A.2A

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Joe had a summer job that pays $7.00 an hour and he worked  between 15 and 25 hours every week. His weekly salary can be  modeled by the equation:   y = 7x, where y is his weekly salary and  x is the number of hours he worked in a week. What is a reasonable domain for this function?

• {15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}

• {105, 112, 119, 126, 133, 140, 147, 154, 161, 168}

• {x | 15 ≤ x ≤ 25}

• {x | 105 ≤ x ≤ 168}

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