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:
- independent variable
- independent quantity
- dependent variable
- dependent quantity
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 = 15x + 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.