1. Today in Precalculus Go over homework Notes: Limits with infinity
and Asymptotes
Homework

2. Limits and asymptotes
The line x = a is a vertical asymptote of the graph of a
function y = f(x) if f(x) approaches a limit of +∞ or -∞
from either direction
The line y = b is a horizontal asymptote of the graph of a
function y = f(x) if f(x) approaches a limit of b as x
approaches +∞ or –∞

3. Infinity as the limit
Vertical Asymptote: x = 0 ∞ ∞ ∞

4. Infinity as the limit
VA: x = 2 -∞ ∞
DNE

5. Limits and Vertical Asymptotes
Simplify equation
If term in denom goes away, hole at denom = 0
If term does not go away, VA at denom = 0
hole at x = 2
VA: x = -3

6. Limits with Infinity (end behavior)

7. Limits with Infinity (end behavior)
HA: y = 0
No VA or holes

8. Limits with Infinity (end behavior)
HA: y = 2 2
No VA or holes

9. Limits with Infinity (end behavior)
HA: none ∞ -∞
VA: x=1, x=-1
Holes:none