Determine Where a Function is Increasing, Decreasing, or Constant
Now that we have more practice graphing and working with equations of functions, we will learn how to describe the behavior of a function over a large interval or by zooming in on a local area where the function's behavior changes.
Analyzing the Toolkit Functions for Increasing or Decreasing Intervals
We will now return to our toolkit functions and discuss their graphical behavior in Figure 10, Figure 11, and Figure 12.
Function | Increasing/Decreasing | Example |
Constant Function |
Neither increasing nor decreasing |
|
Identity Function |
Increasing |
|
Quadratic Function |
Figure 10
Function | Increasing/Decreasing | Example |
Cubic Function |
Increasing |
|
Reciprocal |
||
Reciprocal Squared |
Figure 11
Function | Increasing/Decreasing | Example |
Cube Root |
Increasing | |
Square Root |
Increasing on | |
Absolute Value |
Figure 12