Domain and Range of Word Problems

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}

What is the domain of the graphed function?

• -10 < y < 14 where f(x) is all integers

• 0 < x < 8 where x is all non-negative integers

• 0 < x < 10 where x > 0

• 0 < y < 8 where f(x) is all whole numbers

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

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

What is the range of the function?

• R:{y is less than or equal to 3}

• R:{y is greater than or equal to 3}

• R:{all real numbers}

• R:{y is between and including -6 and 3}

Select TWO correct answers.

Domain

​ (a)  

Range

​ (b)  

• The domain of the function is {0,1,2,3,4,5}

• The range of the function {0,96,192,288,384,480}

• The domain of the function is all real numbers

• The domain of the function {0,96,192,288,384,480}

• The range of the function {0,1,2,3,4,5}

• The range of the function is all real numbers.

A student borrowed $480 from a friend. He agreed to make monthly payments of $96 with no interest until the loan balance was paid off. The function shown models this situation, where f(x) represents the remaining loan balance in dollars after the student has made x monthly payments. Which statements are true about the domain and range of the function for this situation? Select the correct answers.

• D: {0, 1, 2, 3, 4, 5}

• R: {0, 96, 192, 288, 384, 480}

• D: all real numbers

• R: {0, 1, 2, 3, 4, 5}

• {0, 96, 192, 288, 384, 480}

• D: {0, 96, 192, 288, 384, 480}

• R: all real numbers

Answer explanation

Domain - x values

Range - y values

Real-world examples = apply common sense and judgements

What is the range of this function?

• (-5, 5)

• (-3, 3)

What is the range of this function?

• (-∞,∞)

• (-4,2]

• (-∞,2]

• [2,-∞)

Find the Range.

• All Real numbers

• 0 < y < 11

• y ≥ 0

• y > 0