Greetings math peeps and welcome to MathSux! In todays post we will be exploring how to tell something is a function or not. Weâ€™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, donâ€™t forget to check out the video and practice problems at the end of this post to practice your skills! Happy calculating! đź™‚

**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 â€śmachine.â€ť

Letâ€™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. Letâ€™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!

**Practice Questions:**

Identify if the following are functions or not and explain your reasoning.

**Solutions:**

Looking to learn more about Algebra? Check out the algebra lessons page here. Thanks for stopping by and happy calculating! đź™‚

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