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Kansas State Polytechnic

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:
Finding the intercepts

 


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:
Finding the vertical asymptote

 


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:
Finding the end behavior


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:
Graph f(x)

 


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:
Example g(x)

 


 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:
Example h(x)

 


 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:
Example F(x)