powerpoint for Algebra 2

1. Rational Functions Module 13 Overview Topic 13.1 Introduction to Rational Functions Graphing Rational Functions Vertical and Horizontal Asymptotes Topic 13.2 Multiplying and Dividing Rational Functions

2. A rational functions is a functions that can be written in the form of a polynomial divided by a polynomial. Where q(x) can not equal zero. Examples: 1. 2. 3. 4. Simplify each expression.

3. 1. 2.

4. 4. 3.

6. Graphing Rational Expressions. Find the Vertical and Horizontal Asymptotes. State the domain and range. Example # 1 Set the denominator equal to 0. There are two vertical asymptotes for this function x = 0 and x = 2.

7. To find the horizontal asymptote compare the degree of the numerator to the degree of the denominator. The numerator is greater therefore the Horizontal asymptote is y = 0. Now lets graph it. Type the equation and be sure to ( ) around the denominator. It might be hard to see the vertical asymptote. Go to the table and look at the x and y values. Where the Error is are Vertical Asym.

8. It is your turn. Graph the following and state the asymptotes if they occur And state the domain and range.

9. Set the denominator equal to zero. Two vertical Asymptotes x = 4 and x = -1. The horizontal Asymptotes is y = 0 because the degree of the Bottom is bigger. Now the graph is below.

10. Multiplying and Dividing Rational Functions. Example # 1 To solve this expression you need to factor each numerator and each denominator.

11. Division To solve use same, change, flip method.

12. Now try these problems. 1. 2.

13. Solutions

14. Solution

15. Questions: