How do I find the Domain, Range, and Function

Question

On a particular day, you arrive at a gas station that only sells regular unleaded fuel, no other options. At your pump, you input exactly 7.870 gallons of gas into your tank and are charged $29.58. You notice your friend is pumping gas at the pump across from you, and they also input exactly 7.870 gallons of gas into their tank and are charged $22.33.

Courtney, your job is to explain to the gas station manager why or why not this gas station is fair using mathematical terms such as function, domain, and range. Consider the following in forming your mathematical explanation to the manager.

What is the domain?
What is the range?
Would this relation represent a function?

Answer 1

Well, what is a function? There is one output value for every input value. For example, if y = √x and x = 36, we know that y = 6 and -6, so y = √x is not a function.

 

When you buy gas, the total is the price per gallon times the number of gallons, right? Since the price per gallon is set, the variable is the number of gallons put in the tank. The number of gallons is our domain, and the total price is our range.

 

To explain to the gas station owner, we say the total should be a function. Since only one type of gas is sold, the price per gallon should be the same on each pump; therefore, each value in the domain (number of gallons) should lead to one value in the range (total price).

 

Buuuuuut, we each have matching x-values, 7.870 and our y-values are different. This means the total is NOT a function, which makes no sense when buying gas. Since the price per gallon is not mentioned, we don't know if only one, or both, of us were charged incorrectly!