Odd and Even Functions (函数.ppt

文档介绍：FUNCTIONS
Symmetric about the y axis
Symmetric about the origin
2
-7
-6
-5
-4
-3
-2
-1
1
5
7
3
0
4
6
8
7
1
2
3
4
5
6
8
-2
-3
-4
-5
-6
-7
So for an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.
Even functions have y-axis Symmetry
2
-7
-6
-5
-4
-3
-2
-1
1
5
7
3
0
4
6
8
7
1
2
3
4
5
6
8
-2
-3
-4
-5
-6
-7
So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph.
Odd functions have origin Symmetry
2
-7
-6
-5
-4
-3
-2
-1
1
5
7
3
0
4
6
8
7
1
2
3
4
5
6
8
-2
-3
-4
-5
-6
-7
We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function.
x-axis Symmetry
A function is even if f( -x) = f(x) for every number x in the domain.
So if you plug a –x into the function and you get the original function back again it is even.
Is this function even?
YES
Is this function even?
NO
A function is odd if f( -x) = - f(x) for every number x in the domain.
So if you plug a –x into the function and you get the negative of the function back again (all terms change signs) it is odd.
Is this function odd?
NO
Is this function odd?
YES
If a function is not even or odd we just say