What Are Mathematical Functions?

A Function is a math machine. There are inputs (domain), and outputs (range).

When you add an input you get exactly one output. You can not have anymore than one output per input. How you can test this is with the vertical line test where you look along the X axis and see if there is two point overlapping vertically. If there is then that equation is not a function but if there is only one point at a time, then it passes the vertical line test.

In a function Y can be represented as f(x). Therefore when we see something in side of the parenthesis we know that it is changing the X value.