Today in Precalculus

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 8 or -8 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 8 or 8
3
Infinity as the limit
Vertical Asymptote x 0

• 8

8
8
4
Infinity as the limit
VA x 2

• -8

8
DNE
5
Limits and Vertical Asymptotes

1. Simplify equation
2. If term in denom goes away, hole at denom 0
3. 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

• 0

0
No VA or holes
8
Limits with Infinity (end behavior)
HA y 2

• 2
• 2
• No VA or holes

9
Limits with Infinity (end behavior)
HA none

• 8
• -8

VA x1, x-1 Holesnone