# Applying Domain & Range in Real World Settings

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• 2:03 Real-World Settings
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we'll review the domain and range of a function. Then, we'll look at examples of applying the domain and range in real-world settings and explore the information that the domain and range can provide in day-to-day situations.

## Domain and Range

Let's start with an example. Suppose the gas tank in Zack's car holds 20 gallons of gas, and the car gets 32 miles per gallon. Zack fills up his tank with gas and heads out on a trip. His distance (or D) traveled on one tank of gas can be represented by the function:

 D(x) = 32x, where x is the number of gallons of gas he used

The formula would be D(x) = 32x, with 0 less than or equal to x, which is less than or equal to 20.

In this function, the number of gallons used can be anywhere from 0 gallons to 20 gallons, since the tank holds 20 gallons of gas. Based on this and the fact that the car gets 32 miles per gallon, Zack can drive anywhere from 0*32 = 0 miles to 20*32 = 640 miles on one tank of gas.

Mathematically speaking, the number of gallons Zack can possibly use would be the domain of the function, and the possible number of miles traveled would be the range of the function. The domain consists of the values that can be put into a function that make sense (that is, values that don't make the function undefined). In other words, Zack can put up to 20 gallons into his tank: It wouldn't make sense to put 21 gallons in because one would spill out. The range of a function is the set of values that come out of a function based on the function's domain.

Let's take a look at our function D(x) = 32x and put this into context. As we said, the domain is the possible number of gallons of gas used. This is represented by x in the function, or the input value. Makes sense, doesn't it? The input values are the domain of the function, so the number of gallons used is the domain. Similarly, the output values, or D(x), represent the range, so the range is the possible distance traveled.

## Real-World Settings

To apply the domain and range in real-world settings, we take a function that represents a real-world situation and then analyze what the domain and range represent in the function. This allows us to apply the domain and range in a real-world setting.

Consider the following scenario. You're throwing a surprise birthday party for a friend of yours. You head to the store with \$15 in your pocket to buy some chips to go with a dip you made. When you get there, you see that each bag of chips costs \$3. So, the number (or N) of bags of chips you buy can be represented by the function N(x) = x / 3, where x is the amount of money you can spend.

This is an interesting example, because there are a few things to consider. First, let's talk about the function's domain. In the function, N(x) = x / 3, the domain consists of all values of x that we can plug in the function. Just looking at the function , it would appear that x can be any real number. However, if we put our function into the context described, the domain is limited. We saw that you only have up to \$15 to spend. Therefore, we can only plug values from 0 to 15 into the function.

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