A function is a set of data that has one distinct output for each input, but functions are much more than x and y living together on a Cartesian plane in a graph paper galaxy. They have applications in real life. Functions describe the relationship between an input and its output.

Graphs, charts, equations, and verbal descriptions – these depict functions.

Here are other words for input and output:

### Input:

*x*-value- independent variable
- independent quantity
- domain
- cause

### Output:

*y*-value- dependent variable
- dependent quantity
- range
- effect

As you have probably surmised, you control the input. Once the input travels through the function, you get your output. OK, I’m a big math nerd, but I will leave Algebra land to explain.

Imagine that you’re running late for math tutoring. You’re speeding 60 miles per hour in a 20 mile per hour school zone. A cop pulls you over and writes you a $300 speeding ticket. Let’s break down this real world cause and effect situation.

**Input:** You chose to exceed the speed limit by 40 miles per hour.**Output:** You received a speeding ticket.

You see, you can control how fast you’re going, but the consequence, or the output, is up to the cop.

### Algebra That’s Useful During March Madness

Let me give you another example. I have a perfect function that determines basketball scores. (Shhh…It’ll be our secret.)

*y* = 15*x* + 10*x* is the number of hours per day that a basketball team practices.*y* is the number of points scored in the game.

For a breakdown of the results in a table, refer to the Basketbal Scores Table.

For a depiction of the results in a graph, look at the Basketball Scores Graph in More Images.