1. Graphs of Rational Functions
2.6
Graphs of Rational Functions

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
Rational Functions
Transformations of the Reciprocal Function
Limits and Asymptotes
Analyzing Graphs of Rational Functions
… and why
Rational functions are used in calculus and in scientific
applications such as inverse proportions.

5. Rational Functions

6. Asymptotes Asymptotes:
Rational functions have horizontal and vertical asymptotes.
Vertical Asymptotes occur where the denominator = 0.
Horizontal asymptotes occur as x goes to
Graph y=1/x and identify the asymptotes

7. Limit Notation Right Side and Left Side of Numbers

8. Example 1 Finding the Domain of a Rational Function

9. Example 2

10. Example 3A Finding Asymptotes of Rational Functions
Look at the graph on your graphing calculator.

11. Graph a Rational Function

12. Graph a Rational Function

13. Example 3B Finding Asymptotes of Rational Functions
Slide 2- 13

14. Examples using Graphing Rules

15. Example 5 Graphing a Rational Function

16. Example 6 The homework says “analyze” in #37-40.
Precalculus Notes 2.6
Example 6
The homework says “analyze” in #37-40.
Just do intercepts and asymptotes and sketch.

17. Example 4