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Graphing Rational Functions

Graphing Rational Functions

Author: Sarah Kummeth
Description:

Learn how a, h and k affect the graph of a function.

In this packet you will learn how a, h and k each affect the graph in a rational function. The movie on 'a' explains shifts of h and k. The next videos are examples of shifting asymptotes of h and k.

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Tutorial

What's The Reason For All These Letters?

Things to Remember About Graphs of Functions with Only a Change to 'a'

  • The larger 'a' is, the farther away the branches of the hyperbola will be from the asmyptotes. The branches of the hyperbola will look smaller if 'a' is a larger number.
  • If 'a' is a fraction, the branches of the hyperbola will be closer to the asmyptotes, therefore making the branches look larger.

How 'a' Affects the Graph of a Rational Function

Steps to How 'h' Affects the Graph of a Function

1. Draw table and Graph

2. Where is your a, h and k?

3. Will the asmyptotes shift? If so, in what direction? Draw in these shifts if applicable.

4. Pick numbers to put in for x to evaluate for y. Don't forget to use positives, negatives and fractions.

5. Substitute your x values in and solve for y.

6. What is your domain and range? ( if you get undefined when placing in an x value, this is your domain for x which is where h lies on the graph.) (range would involve k in the problem.)

7. Plot points found. 8. Draw a smooth connected line (or try) through all the points. You now have graphed hyperbolas for a rational function!

How 'h' Affects the Graph of a Rational Function

THERE IS NO SOUND, DON'T WORRY.

Steps to How 'k' Affects the Graph of a Rational Function.

1) Set up your table and graph.

2) Identify the shifts that will occur in your graph. These will also be domain and range. h (orginates from where y axis is) being domain and k (originates from where x axis is) being range. Draw in the identified asymptote(s).

3) Put in values for x.

4) Solve for y with these values.

5) Plot points.

6)Connect together points with lines.

7) You have now graphed hyperbolas for a rational function.

How 'k' Affects the Graph of a Rational Function

THERE IS NO SOUND.

Graphing a Rational Function with a, h and k