1. Pre-Calculus Go over homework End behavior of a graph
Notes: Increasing and Decreasing Intervals
Practice

2. Asymptotes
Asymptotes: vertical or horizontal lines the graph of a function does not cross
This graph has:
two vertical asymptotes at x=-1 and x=2
one horizontal asymptote at y=0 as x approaches -∞,∞

3. End Behavior
Used to describe the behavior of a graph as x approaches ∞ and -∞.
Describes what is happening to y-values at the left and right ends of the graph.
Limit notation is used to describe end behavior:
In the example:

4. Example 1
End behavior:
Asymptotes:
Horizontal: y=1
Vertical: x=2

5. Example 2
End behavior:
Asymptotes: Horizontal y=2

6. Example 3
End behavior:
Asymptotes:
Horizontal y=2, y=-4
Vertical: x=0

7. Increasing/Decreasing
Can visually determine if a function is increasing, decreasing, or constant.
A function is:
increasing on an interval if, for any two points in the interval, a positive change in x results in a positive change in f(x).
decreasing on an interval if, for any two points in the interval, a positive change in x results in a negative change in f(x).
constant on an interval if, for any two points in the interval, a positive change in x results in a zero change in f(x).

8. ( - ∞, - 5 ) υ ( - 1, 2 )
(- 3, - 1 ) υ ( 2, ∞ )
(- 5, - 3 )

9. ( 1, ∞ )
( - ∞, ) υ ( 3.464, ∞ )
( - ∞ , 1 )
( , - 2 ) υ( - 2, 2 )υ( 2, 3.464)
none
none

10. ( - ∞, 2 )
( 1, ∞ )
( 4 , ∞ )
( - ∞, -1 )
(2, 4 )
(-1, 1 )