1. Graphing Rational Functions Part 2
Precalculus 12.2

2. Ex.
What is the end behavior for ?
horizontal asymptote

3. What is the end behavior for ?
Ex.
What is the end behavior for ?
slant asymptote
notice that the difference in degree between numerator and denominator is 1

4. Ex.
What is the end behavior for ?
slant asymptote

5. What is the end behavior for ?
Ex.
What is the end behavior for ?
parabolic asymptote
notice that the difference in degree between numerator and denominator is 2

6. If the limit to infinity of a function:
is a number
goes to infinity with a degree difference of 1
goes to infinity with a degree difference of 2
horizontal asymptote
slant asymptote
parabolic asymptote

7. long division of polynomials
How do we find the equation of the asymptote?
long division of polynomials

8. Ex. Describe the end behavior and find the
equation of the asymptote for
slant asymptote

9. Let’s put it all together…

10. Zeros Holes VA End Behavior
Ex. For the given function, identify the zeros, holes, vertical asymptotes and end behavior. Sketch the graph and label.
hole
Zeros
Holes VA
End Behavior

11. End Behavior:
Slant asymptote:

12. Zeros Holes VA End Behavior
Ex. For the given function, identify the zeros, points of discontinuity by category and end behavior. Sketch the graph and label.
Zeros
Holes VA
End Behavior

13. For your fun and enjoyment…