1. PRE-CALCULUS Rational Functions

2. Simple Rational Functions Appears in the following format: Has 2 asymptotes: x=h (vertical) y=k (horizontal) In order to graph: Draw the lines for the asymptotes. Select two points on each side of every asymptote, plug into your x/y chart and graph.

3. Simple Rational Function Practice Determine all of the asymptotes for each graph:

4. Simple Rational Function Practice Determine all of the asymptotes AND graph:

5. Need Mo Practice? Of course you do fool! With your partner, complete #1-4 on pg. 32 of your workbook.

6. Complex Rational Functions Appears in the following format: In order to graph: Draw the lines for the asymptotes. Select two points on each side of every asymptote, plug into your x/y chart and graph. Asymptotes/Quirks: Can have multiple vertical asymptotes. Can have multiple horizontal asymptotes. Might have holes.

7. Complex Rational Functions Appears in the following format: Asymptotes/Quirks: Can have multiple vertical asymptotes. How to Determine VA’s 1. Factor the numerator and denominator. 2. Determine what values would make the denominator equal to 0.

8. Vertical Asymptote Practice

9. Complex Rational Functions Appears in the following format: Asymptotes/Quirks: Can have multiple horizontal asymptotes horizontal asymptotes. How to Determine HA’s 1. Look at the degrees of the numerator and the denominator. 2. Follow and memorize the guide on the next slide.

10. Horizontal Asymptote Guide

11. Horizontal Asymptote Practice

12. Complex Rational Functions Appears in the following format: Asymptotes/Quirks: Might have holes. How to Find Holes 1. Factor the numerator and denominator. 2. If there is a common factor in the numerator and the denominator, set it equal to zero. Solve and the value you find is the x-coordinate of the location your hole occurs at.

13. Diggin’ Holes Practice

14. Putting it All Together Appears in the following format: In order to graph: Draw the lines for the asymptotes. Select two points on each side of every asymptote, plug into your x/y chart and graph. Determine if there are holes and graph them accordingly.

15. Graphing Practice

18. Homework Complete Pg. 27-28 in your workbook #1-7. Please find: Vertical Asymptotes Horizontal Asymptotes Holes

19. How do we recognize rational function graphs? Simplify!! Look for the vertical asymptotes Look for horizontal asymptotes Look for holes Match up the function that works for all the asymptotes/holes

20. Matching Around the Room Your sheet of paper contains all the rational functions that are posted around the room Match up the correct function with each picture (pictures are labeled with letters, functions are labeled with numbers) REMEMBER: Look for your asymptotes and holes to eliminate possibilities!