1. Horizontal Asymptotes

2. There are asymptotes at 3 and -6.
Vertical Asymptotes
Last time, we learned about vertical asymptotes, and that they are determined by the denominator of a rational function.
There are asymptotes at 3 and -6.

3. Determine the vertical asymptotes.

4. Horizontal Asymptotes
To find a horizontal asymptotes, we focus on the degree of the numerator and the denominator.
What’s the degree?
What’s the degree?

5. How do we use degrees to find the horizontal asymptote?
BOBO BOTN EATS DC

6. BOBO Bigger On Bottom, y = O
Degree of 3
Degree of 5
The degree is bigger on the bottom, so the horizontal asymptote is the line y = 0.

7. BOTN
Bigger On Top, No HA
Degree of 6
Degree of 3
The degree is bigger on the top, so there is no horizontal asymptote.

8. Exponents Are The Same, Divide Coefficients
EATS DC
Exponents Are The Same, Divide Coefficients
Degree of 3
Degree of 3
The degrees are the same, so divide the leading coefficients. The horizontal asymptote is y = 2.

9. Find the horizontal asymptotes!

10. Quick Recap! Vertical Asymptote Horizontal Asymptote
Use the denominator of the fraction. Determine what values of x make the denominator = 0.
Find the degree of the numerator and denominator.
Use BOBO BOTN EATS DC to find the horizontal asymptote.