Function Application for the Real World

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  • 0:03 Functions
  • 2:07 Functions in the Real World
  • 3:05 Examples
  • 4:46 Lesson Summary
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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 recall what a function is and then look at applying functions in real life that involve both numbers and objects. We'll then learn how to solve problems using these functions.


Do you have a different outfit that you wear each day of the week? If so, you might be surprised to learn that the relationship between the day of the week and your outfit represents a mathematical concept called a function.

Day Outfit
Sunday Plaid Skirt, Brown Blouse
Monday Jeans, Gray Sweater
Tuesday Jean Shorts, Green T-shirt
Wednesday Gray Slacks, Black Blouse
Thursday Flowered Dress
Friday Blue Shorts, White Sweater
Saturday Sweatpants and Sweatshirt

In mathematics, a function is a relationship between two sets of elements in which no element in the first set relates to more than one element in the second. We can think of a function as a rule that takes inputs from the first set and relates them to an element in the second set, which is the output.

In mathematics, we represent functions in many different ways; we can use words, tables, mappings, equations, and even graphs. Consider this example: If a state has a 6% sales tax, then we can use a function to calculate it. We can use the following equation to represent this function:

T = 0.06x

If we purchase a product for x dollars, then to calculate the tax, we would multiply x by 0.06, or the tax rate in decimal form. For instance, if you bought a shirt for $25, then you can calculate the sales tax by plugging in 25 for x.

T = 0.06(25) = 1.5

We see the sales tax is $1.50.

We can also represent this function using our other representations. Because our purchase price can be any number, we could never list all of the inputs and outputs! Using a table or mapping wouldn't be the best method in this situation, but we can easily represent it graphically by simply graphing the equation T = 0.06x.

We see that there are many ways to represent a function, and each one depends on its context. Now that we are reminded what a function is in mathematics, let's talk some more about using them in real-world settings!

Functions in the Real World

When it comes to recognizing functions in the real world, it is useful to think of the term ''is a function of'' as ''is determined by.'' You see, in a function, no input can be related to two different outputs, otherwise, given the input, we couldn't determine the output. Therefore, the input determines the output, so the output is a function of the input.

For instance, think about those outfits again.

Day Outfit
Sunday Plaid Skirt, Brown Blouse
Monday Jeans, Gray Sweater
Tuesday Jean Shorts, Green T-shirt
Wednesday Gray Slacks, Black Blouse
Thursday Flowered Dress
Friday Blue Shorts, White Sweater
Saturday Sweatpants and Sweatshirt

If it's Tuesday, what outfit will you be wearing? Well, we look to see what outfit to which Tuesday is mapped, and we see that you will be wearing your jean shorts with your green t-shirt. That's not too hard, is it? You can see that your outfit ''is determined by'' the day of the week, so your outfit ''is a function of'' the day of the week.

Pretty neat, huh? You may have been familiar with functions involving numbers, but it's totally cool to see that the function concept can actually be applied to real world situations! Let's consider a couple more examples!

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