1. Rational Functions of the Form

2. For this model, both the numerator and the denominator are linear expressions. We are getting close to maximum complexity…

3. Examine the following Vertical asymptote at x = 2. What about the horizontal asymptote?

4. As x approaches infinity,…. Both the numerator and denominator approach infinity, which can make it tricky to figure out… We will operate algebraically first…

5. Divide each term by x Now, as x approaches infinity, this term gets very close to zero

6. So, as

7. likewise, as

8. The function approaches the line y = 1 for both directions. So, y = 1 is the equation of the horizontal asymptote. (this makes the intercepts easier to find)

10. Intercepts? When x = 0, y = ? When y = 0, x = ?

12. At this stage, it may be easier to pick a few points near the asymptotes…

13. Examine the following model using the DIVER structure:

14. Sketch specifics: Domain Intercepts Vertical asymptote End Behaviour Range

15. Pg 174 1a,c,e 2a,c,e 3a,c,e DIVER on 3 10

16. End Behaviour as