1. Family Functions: Increasing and Decreasing End Behavior

2. We read graphs from left to right, just like a book!

3. Increasing or Decreasing?
Both!

4. Notation
We write where our graphs are Increasing or Decreasing in interval notation – similar to writing the Domain and Range.
However, we do not use the brackets “[ ]” because at the point of change, it is neither increasing or decreasing.
If we have more than one increasing/decreasing section of our graph, we combine the intervals with a “U”, which represents the union of the two intervals.

5. Increasing
Start from the left and look at the sections of the graph that are increasing (y-values getting larger).
{-∞, -3) U (1, 4)

6. Decreasing
Start from the left and look at the sections of the graph that are decreasing (y-values getting smaller).
(-3, 1)

7. Constant
Start from the left and look at the sections of the graph that are flat – neither increasing or decreasing (y-values stay the same).
(4, ∞}

8. (-5, -3) U (-1, 1) U (4, 5)
Increasing:
Decreasing:
Constant:
{-∞, -5) U (1, 4)
(-3, -1) U (5, ∞}

9. End Behavior
We can look at the ends of our graphs and determine what the rest of the graph will look like.
We say, “As x  ∞, f(x)  ?
x DOES NOT have to “go to” infinity. If the graph ends in point rather than arrows, then it is “as x goes to (the point)”

10. 7
As x  9, f(x) _____
As x  -∞, f(x)  _____ 7 9 -∞