​Function

A Vertical Line

cuts the graph in 1 point only

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​so this IS A FUNCTION!

​Not a Function

​A Vertical Line

cuts the graph in 2 points

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​so this is NOT A FUNCTION.

​Not a Function

​A Vertical Line

cuts the graph in 2 points

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​so this is NOT A FUNCTION.

​Not a Function

Previously, ​we used a Vertical line test to determine that this is not a function.

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That is because if we put 3 as an input, we can get 1.732 or -1.732 as a result, so we don't know which one is the right answer.

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So, if 1 input has 2 different outputs, it is not a function.

​Function

​A function has unique output for each input.

​Function

​A function has unique output for each input.

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​No matter how many times I put the same input in, I should always get the same result.

​Function

​This IS A FUNCTION, because both b and c each have one result only. I don't care that those are the same value.

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​All I care about is that

each time I put b I'll get y and

each time I put c in, I'll get y.

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​Our rule (function) is consistent.

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​Not a function

​3 maps in 4 and 5

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​This rule is not consistent, so it's not a function.

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Or for the same input we don't get a unique result.

​To sum up

​A relation is a function if each input has only one output!