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# What is a function?

by MathyCathy## — 41521

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Play this *FLASH*
"Function Machine" game
to explore relationships between inputs and outputs.
www.mathplayground.com
Algebraic thinking with a function machine.

Function Notation and Evaluating Functions
www.regentsprep.org
Evaluating Functions and Function Notation

A function is a relationship such that every input has exactly one output.
www.mathsisfun.com
What is a Function

In a function, for every "x" there is only one "y".

In a function, for every domain value there is only one range value.

Practice Quiz - Identifying Functions (with feedback for you!)
www.thatquiz.org
Relations and Functions Practice Quiz

"x" is the INDEPENDENT variable.

"y" is the DEPENDENT variable.
"y" DEPENDS ON "x".

Students may first learn about functions as a type of "machine".
Put something into the machine, the machine follows a rule, and something new comes out of the machine.

A "function rule" in algebra describes an equation.
Choose an input for "x", perform the "rule" and get the output "y" or "f(x)".
We read this function notation as "f of x".

Inputs and outputs can be organized using a table.

Inputs (domain values) and outputs (range values) can be visually organized using a mapping diagram.

Functions can be represented as graphs. Generating a set of points from a function rule can result in pictures like these.

Quiz: Function Rules, Tables and Graphs (with feedback for you!)
www.thatquiz.org
Function Rules, Tables, and Graphs

This table could also be represented as a set of ordered pairs.
{(-2, -3) , (-1, -1) , (0, 1) , (1, 3) , (2, 5)}
Most folks prefer organizing a set of ordered pairs using a table. It's easier to see the inputs and outputs that way.

Created by
Cathy Yenca
www.mathycathy.com

What is a Function?<br />Watch the first 5 minutes.<br />
www.youtube.com
The first lecture in Jim Fowler's upcoming MOOC course, Calculus One on Coursera. Class begins 1/7/2013. Visit: http://go.osu.edu/mooculus to learn more and ...

Functions
www.youtube.com
Functions can be thought of as mathematical machines, which when given an element from a set of permissible inputs, always produce the same element from a se...

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