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Ms. Russell's Guides
Linear Functions


What is a Function?   The Definition of a Line   The Big Deal with Slopes   How Can I remember?   Putting It Together   Quiz Yourself

What is a Function?

A function is a relation in which every input value can have only one output value.

In other words
For every "x" there is only one "y"

and that means

It Passes the Vertical Line Test

To use the Vertical Line Test, simply draw imaginary vertical lines through your graph. If a vertical line passes through more than one spot on the graph, then it fails and is not a function. If it only passes through once, then it passes and is a function.

Examine the relations below:
relations

What do these graphs have in common?
What's different?
Can you group any of them?
answer

How can you test these graphs to show if they are or are not functions?
answer


Still Confused?  Try this out...


This is a Function Machine

function machine
To use this machine, we put a number in to the "INPUT" screen.
The machine will take your function, do the calculations and the final result shows up in the "OUTPUT" screen.


It is key to know: If it is a function, then each number that you input will give you only one result!


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