Section 1 5 more on functions and their graphs
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Section 1.5 More on Functions and Their Graphs PowerPoint PPT Presentation


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Section 1.5 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.

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Section 1.5 More on Functions and Their Graphs

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Section 1 5 more on functions and their graphs

Section 1.5 More on Functions andTheir Graphs


Increasing and decreasing functions

Increasing and

Decreasing Functions


Section 1 5 more on functions and their graphs

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


Section 1 5 more on functions and their graphs

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

Example


Section 1 5 more on functions and their graphs

Example

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


Section 1 5 more on functions and their graphs

Example

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


Relative maxima and relative minima

Relative Maxima

And

Relative Minima


Section 1 5 more on functions and their graphs

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

Even and Odd Functions

and Symmetry


Section 1 5 more on functions and their graphs

Example

Is this an even or odd function?


Section 1 5 more on functions and their graphs

Example

Is this an even or odd function?


Section 1 5 more on functions and their graphs

Example

Is this an even or odd function?


Piecewise functions

Piecewise Functions


Section 1 5 more on functions and their graphs

Example

Find and interpret each of the following.


Section 1 5 more on functions and their graphs

Example

Graph the following piecewise function.


Functions and difference quotients

Functions and

Difference Quotients


Section 1 5 more on functions and their graphs

See next slide.


Section 1 5 more on functions and their graphs

Continued on the next slide.


Section 1 5 more on functions and their graphs

Example

Find and simplify the expressions if


Section 1 5 more on functions and their graphs

Example

Find and simplify the expressions if


Section 1 5 more on functions and their graphs

Example

Find and simplify the expressions if


Section 1 5 more on functions and their graphs

Example


Section 1 5 more on functions and their graphs

(a)

(b)

(c)

(d)


Section 1 5 more on functions and their graphs

(a)

(b)

(c)

(d)


Section 1 5 more on functions and their graphs

(a)

(b)

(c)

(d)


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