1. 3.3 More on Functions; Piecewise-Defined Functions
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2. Increasing Intervals
If we trace the graph of a function from left to right and the values f (x) increase as shown in the figure, we say that the function is increasing on the interval (a, b).

3. Decreasing Intervals
If the values f (x) decrease as in the figure, we say that the function is decreasing on the interval (a, b).

4. Constant Intervals
If the values f (x) remain unchanged as x increases, we say that the function is constant on the interval (a, b).

5. Example 1
State the open intervals on which the function is increasing or decreasing.

6. Example 2

7. Local Maximum and Local Minimum
We call the y-value of a “high point” a local maximum, and we call the y-value of a “low point” a local minimum.

8. Local Maximum and Local Minimum
A local maximum occurs where the function changes from increasing to decreasing.
Similarly, a local minimum occurs where the function changes from decreasing to increasing.

9. Example 3
Locate the local maxima and local minima using the graph of the function shown.

10. Example 4
Locate the local maxima and local minima using the graph of the function shown.

11. Piecewise Function
Some functions, called piecewise-defined functions, are defined by using different equations for different intervals in their domains.

12. Example 5
Use the piecewise-defined function shown to find each of the following:
f(-5)
f(1)
f(2)