How to Tell if Something is a Function?

Greetings math peeps and welcome to MathSux! In todays post we will be exploring how to tell something is a function or not. We’ll start off by defining what a function is, go over its notation, and then look at several different examples of how to recognize a function in different formats including function maps, tables, and graphs! Functions are a concept that is seen throughout algebra and mathematics so understanding it well is key to learning more! Also, don’t forget to check out the video and practice problems at the end of this post to practice your skills! Happy calculating! 🙂

What is a Function?

A function works like a machine with inputs and outputs. When we input a number into a function, a new number pops right back out. We can say that a function is like a machine because it transforms one number into a completely different number once it enters this so called “machine.”

Let’s look at an example in action, where f(x)=2x+1 is the function and we want to see what happens when we plug inout a 3 into our function.

Notice we plugged in 3 into the variable x and solved, to get the output 7.

Function Notation:

Functions have their own notation, when we have f(x)=2x+1, this can also be written as g(x), h(x), or any other letter you can think of!

In the previous input/output example, the input value 3 is plugged into the function f(x)=2x+1 for the missing variable, x to get the output 7.

Another way to write what we did in function notation is to say that we found the value for f(3)=6 for the function f(x).

How to Tell if Something is a Function?

A main and important rule of functions is that there is always one unique input, but there can be different or repeating outputs. Let’s look at some examples below, at how to identify a function.

Example #1:Function Maps

Example #2: Tables

Example #3: Graphs

In order to know if a function is a function when looking at graph, we perform something called a Vertical Line Test. All we must do is draw a vertical line, if the line hits the graph one time, the graph is a function! If the vertical line his more than that, the graph is not a function.

Try the following practice questions to test your skills below!