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Section 1.5 More on Functions and Their Graphs

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Section 1.5 More on Functions andTheir 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? 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)