Section 2.2 More on Functions and Their Graphs

Increasing and Decreasing Functions

The open intervals describing where functions increase, decrease, or are constant, use x-coordinates and not the y-coordinates.

Find where the graph is increasing. Where is it decreasing Find where the graph is increasing? Where is it decreasing? Where is it constant? Example

Example Find where the graph is increasing? Where is it decreasing? Where is it constant?

Example Find where the graph is increasing? Where is it decreasing? Where is it constant?

Relative Maxima And Relative Minima

Where are the relative minimums? Where are the relative maximums? Why are the maximums and minimums called relative or local? Example

Even and Odd Functions and Symmetry

Example Is this an even or odd function?

Example Is this an even or odd function?

Example Is this an even or odd function?

Piecewise Functions

Example Find and interpret each of the following.

Example Graph the following piecewise function.

Functions and Difference Quotients

See next slide.

Continued on the next slide.

Example Find and simplify the expressions if

Example Find and simplify the expressions if

Example Find and simplify the expressions if

Example

(a) (b) (c) (d)

(a) (b) (c) (d)

(a) (b) (c) (d)