1
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.
2
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.
3
Where is the function
increasing?
4
Where is the function
decreasing?
Where is the function
constant?
5
6
7
( ) 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
= − + − < <
8
( ) ( )
12
12
12
12 change of rate Averagexx
xfxf
xx
yy
x
y
−
−=
−
−=
∆
∆=
9
( ) 2Suppose that 2 4 3.g x x x= − + −
A) even
B) odd
C) neither
Is the function shown below even, odd or neither?
10
A) increasing
B) decreasing
C) constant
Is the function below increasing, decreasing or
constant on the interval (0, 1)?