### 0.6 Graphing Rational Functions

1: Introduction to Graphing Rational Functions, Finding the x- and y-intercepts

This video covers:

*Review of what a Rational Function is

*The steps to take to graph a rational function

*Review of how to find the x- and y-intercept, and what format they should be in

*Shortcuts to finding the x- and y-intercepts

*How to know if you don't have any x-intercepts

Examples:

2: Finding the Vertical Asymptotes

This video covers:

*Review of the steps to graphing rational functions

*Definitions of domain and asymptotes

*Images of the vertical, horizontal, and oblique asymptotes

*Which asymptote that a graph cannot cross

*How to find the vertical asymptote and what format it should be in

Examples:

3: Finding the Horizontal and Oblique Asymptotes

This video covers:

*Review of the steps to graphing rational functions

*Review of what the end behavior means

*What is meant by the face case and how it helps to find the end behavior of the graph

*A summary of each of the cases

*What format both the horizontal and oblique asymptotes come in

*How to identify whether it is a horizontal or oblique asymptote

Example:

4: Sketching the Graph and Checking with the Graphing Calculator

This video covers:

*Review of the steps to graphing rational functions

*How to draw all steps on the graph: y-intercept, x-intercept, vertical asymptote, horizontal/oblique asymptotes

*How many parts each graph should contain

*Filling in any missing pieces with extra ordered pairs

*How to check rational functions with the graphing calculator

*The correct way to type rational functions and the standard window on the graphing calculator

*Why you calculator might draw something different than what it actually looks like

Example:

5: Putting All The Steps Together To Graph a Rational Function

This video covers:

*Review of the steps to graphing rational functions

*Working through all the steps of the example below, including putting all answers in the correct format

*Review of the face case to find the end behavior of the graph

*Plotting all necessary information on the graph

*Review of how may parts each graph should contain

*Checking with the graphing calculator, reminding how to type in the function in the correct format

*How the graphing calculator doesn't always show all the details in the standard window

Example:

6: Example of Oblique Asymptote

This video covers:

*Review of the steps to graphing rational functions

*Working through all the steps of the example below, including putting all answers in the correct format

*How to long divide polynomials to come up with the oblique (slanted) asymptote

*Plotting all necessary information on the graph, including how to draw an oblique asymptote

*Review of how may parts each graph should contain

*Checking with the graphing calculator, reminding how to type in the function in the correct format

*How you can graph the oblique asymptote and the graph at the same time on the graphing calculator

Example:

7: Example of a hole in the Graph

This video covers:

*Review of the steps to graphing rational functions

*Working through all the steps of the example below, including putting all answers in the correct format

*How to long divide polynomials to come up with the oblique (slanted) asymptote

*Plotting all necessary information on the graph

*What causes a hole in the graph of a rational function and how to find it

*Checking with the graphing calculator, reminding how to type in the function in the correct format

*How to use your double check specific ordered pairs, including where a hole could be

Example: