1. 2.7 Rational Functions and Their Graphs Graphing Rational Functions

2. 1) Find the y-intercept: Substitute 0 in for x 2) Find the x-intercepts: Set the numerator equal to 0 and solve. 3) Find the Vertical Asymptote: Set the denominator equal to zero and solve. 4) Find the Horizontal or Slant Asymptote: Use the numerator’s degree (m) and the denominator’s degree (n) to determine which method to use. 5) Find Extra Points: Find points to the left and right of each vertical asymptote. 6) Graph: Graph steps 1-6.

3. Degree ComparisonAlternate Asymptote Slant Asymptote: Long Division Horizontal Asymptote:

4. Graphing Rational Functions (m=n) a b

5. c

6. d

7. Graphing Rational Functions (m<n) a b

8. d c

9. e

10. Graphing Rational Functions (m>n) b a

11. d c

12. e

13. Special Rational Functions b a

14. d c

15. e

16. b a

17. d c Horizontal Asymptote:

18. Special Rational Functions e