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Graphing Rational Functions

Part 1

In this video, we are going to graph simple rational functions.

For example: y=\frac{1}{x}

Let’s first make a table listing the x and y values

x y
-3 \frac{1}{-3}
-2 \frac{1}{-2}
-1 \frac{1}{-1}=-1
0 \frac{1}{0}=UNDEFINED
1 \frac{1}{1}
2 \frac{1}{2}
3 \frac{1}{3}

Plot the coordinate points on a coordinate plane. Note how there are no points on the x-axis.

Part 2

In the second video, we are going to graph rational functions with transformation.

Keep the following in mind during transformation:

Add # to x Moves Left
Subtract # from x Moves Right
Add # to Function Moves Up
Subtract # from Function Moves Down
Multiply Function (Positive) Each y-value is multiplied
Multiply by Function (Negative) Each y-value is multiplied, flipped over y-axis

For example:
A transformation from y=\frac{1}{x} to y=\frac{1}{x}+2, each point of the latter graph will be located two units above each point of the prior graph.

A transformation from y=\frac{1}{x} to y=-\frac{1}{x}, each point of the latter graph will be located across the x-axis compared to each point of the prior graph.

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