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Section 3.3

Properties of Functions

For an even function, for every point (x, y) on the

graph, the point (-x, y) is also on the graph.

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So for an odd function, for every point (x, y) on the

graph, the point (-x, -y) is also on the graph.

Determine whether each graph given is an even function,

an odd function, or a function that is neither even nor

odd.

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Where is the function

increasing?

4

Where is the function

decreasing?

Where is the function

constant?

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6

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( ) 3Use a graphing utility to graph 2 3 1 for 2 2.

Approximate where has any local maxima or local minima.

f x x x x

f

= − + − < <

( ) 3Use a graphing utility to graph 2 3 1 for 2 2.

Determine where is increasing and where it is decreasing.

f x x x x

f

= − + − < <

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( ) ( )

12

12

12

12 change of rate Averagexx

xfxf

xx

yy

x

y

−

−=

−

−=

∆

∆=

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( ) 2Suppose that 2 4 3.g x x x= − + −

A) even

B) odd

C) neither

Is the function shown below even, odd or neither?

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A) increasing

B) decreasing

C) constant

Is the function below increasing, decreasing or

constant on the interval (0, 1)?