Real World Domain and Range

A student rode a bike from school to a recreation center. The graph shows the student's distance in miles from the recreation center after riding the bike for x minutes. What is the range of the function for this situation? HINT: what are the smallest and biggest y values the line touches?

• All real numbers greater than or equal to 0 and less than or equal to 28.

• All real numbers greater than or equal to 0 and less than or equal to 9.

• All real numbers less than or equal to 28.

• All real numbers less than or equal to 9.

• { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

• { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

• y ≤ 10

• 0 ≤ y ≤ 10

All of the y values or outputs are called what?

• Domain

• Range

• Relation

• Function

The LNHS Lions stadium seats about 2,000 people. The tickets sell for $6 each. The function f(x) = 6x represents the situation where x is the number of people in attendance and f(x) is the amount of money LNHS makes as revenue. What is the domain of the situation?

• x is all real numbers

• 0 < x < 2,000

• 0 < x < 6 where x is all non-negative integers

• X is the set of all whole numbers < 2,000

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 LNHS Lions stadium seats about 2,000 people. The tickets sell for $6 each. The function f(x) = 6x represents the situation where x is the number of people in attendance and f(x) is the amount of money LNHS makes as revenue. What is the range of the situation?

• 0 < f(x) < 6

• 0 < f(x) < 2,000

• 0 < f(x) < 12,000

• 2,000 < f(x) < 12,000

Pedro is driving to Nevada. The distance d he has left to travel, based on the hours driving h, can be modeled by the function:

d(h) = 2100 - 70h

What does the 2100 tell you?

• the range maximum; it's how fast Pedro is going to drive

• the range maximum; it's how far Pedro is from Nevada at the start

• part of the domain; it's how many hours it will take to get to Nevada

• part of the domain; it's how far Pedro is from Nevada at the start

Pedro is driving to Nevada. The distance d he has left to travel, based on the hours driving h, can be modeled by the function:

d(h) = 2100 - 70h

What kind of numbers can you use for the domain here?

• all positive numbers; the hours just have to be ANY positive number

• all real numbers; the hours can literally be anything

• all positive numbers up to and including h = 30; this is because it takes 30 hours to get there (the function would stop then)

• all positive WHOLE numbers since you can't drive for part of an hour

Pedro is driving to Nevada. The distance d he has left to travel, based on the hours driving h, can be modeled by the function:
d(h) = 2100 - 70h
What kind of numbers can you use for the range here?

• all positive numbers; the miles just have to be ANY positive number

• all real numbers; the miles can literally be anything, including decimals

• the range, which is measuring miles, can be any positive real number (including decimals) up to 2100. The function stops at 2100 miles since he reaches Nevada.