Functions, Domain and Range Word Problems

A gym charges a $15 registration fee and $5 per session. If 𝑥 represents the number of sessions, the total cost for going to the gym is represented by 𝑓(𝑥) = 5𝑥 + 15. Mario will be going to the gym no more than 4 times this week.

What is a possible domain for this situation?

• {1,2,3,4}

• {20,25,30,35}

• {𝑥 | 0 ≤ 𝑥 ≤4}

• {𝑦 | 15 ≤ 𝑦 ≤ 35}

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 a possible range for this situation?

• {1,2,3,4}

• {75,125,175,225}

• {𝑥 | 1 ≤ 𝑥 ≤ 4}

• {𝑦 | 25 ≤ 𝑦 < 225}

A plumber charges a $25 service fee and $50 per hour for at least one hour but not more than 4 hours. If 𝑥 represents the number of hours the plumber is at your house, the total cost for the plumber’s service is represented by 𝑓(𝑥) = 50𝑥 + 25.

What is a possible domain for this situation?

• {1,2,3,4}

• {75,125,175,225}

• {𝑥 | 1 ≤ 𝑥 ≤ 4}

• {𝑦 | 25 < 𝑦 < 225}

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

The graph shown has a domain of​ (a)   .

It has a range of (b)   ​ (c)   (d)   . ​

• ARN

• y

• >

• G

• x

• <

• E

• B

• A

• H

The girls basketball team is having a fundraiser. The girls will receive $5 for each product, p, that they sell. They are required to sell at least 5 items but no more than 10. Is this continuous or discrete and what is the domain/range?

• Discrete

  Domain: {5, 6, 7, 8, 9, 10}

  Range: {25, 30, 35, 40, 45, 50}

• Discrete

  Domain: {25, 30, 35, 40, 45, 50}

  Range: {5, 6, 7, 8, 9, 10}

Match the following

• RANGE

• ALL REAL NUMBERS

• DECREASING

• x < 1

  OR

  x > 3

• NO

  MATCH

• x < 3

  OR

  –1 < x < 2

• DOMAIN

• –3 < x < –1

  OR

  x > 2

• NEGATIVE

• y ≤ 2

The total cost, 𝑐, in dollars to create calendars for a fundraiser can be found using the function 𝑐 = 5.5𝑢 + 25 where u is the number of calendars made. If there are at least 10 calendars made, what is a possible domain for this function?

• {𝑥 | 0 ≤ 𝑥 < 50}

• {−12,−11,12,20,50}

• {𝑥 | 10 ≤ 𝑥 < 100}

• {10,11,12,13,14}