Section 3.3 Properties of Functions 141 section 3-3 notes.pdf · 1 Section 3.3 Properties of...
Transcript of Section 3.3 Properties of Functions 141 section 3-3 notes.pdf · 1 Section 3.3 Properties of...
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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?
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Where is the function
decreasing?
Where is the function
constant?
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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)?