# 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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