Relations

What is a relation?

A relation is anything with input and output values.

What are input and output values?

X-values are inputs and y-values are outputs.

So?

Relations are anything with x and y values.

Functions are a relation with no repeating input values (no repeating x-values)

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Functions

​Because there are 2 arrows that come from the 2 in Set A (the input values) that means this has a repeating x-value!

​​Mapping Diagram

Notice how there are 2 of the number 75 in the High School column (the input values) this means this has a repeating x-value!

​​Table

See how 2 different ordered pairs have a 4 in the x spot? This means this has a repeating x-value!

List of ordered pairs

​Why are these not functions?

Lay your pencil flat on the graph and move it from left to right. If the graph touches your pencil more than once at the same time, it is NOT function.

The graph to the right is not a function because it touches the line more than once at a time, and fails the vertical line test.

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The Vertical Line Test

This graph would touch your pencil twice, and fail the vertical line test

​​Not a Function

This graph does not touch your pencil twice at the same time, and passes the vertical line test

Function

This graph would touch your pencil twice, and fail the vertical line test

Not a Function

This graph does not touch your pencil twice at the same time, and passes the vertical line test

Function

This is a function because each input has only one arrow.

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This is a function!

This is a function because each input has only one arrow.

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This is a function!

This is not a function because 35 has more than one arrow coming from it.

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This is not a function!

This is not a function because 3 has more than one arrow coming from it.

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This is not a function!

This is a function because 7 and -7 are two different numbers, so it has no repeating x-values.

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This is a function!

This is not a function because the input 0 repeats.

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This is not a function!

This is a function because none of the x-values are repeating.

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This is a function!

This is not a function because -4 repeats twice.

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This is not a function!

Parts of a Graph

Graphs usually go on a coordinate plane. This is made up of four quandrants. Starting in the top right corner, they are numbered 1-4.

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​Coordinate Planes