Even Functions
Even functions are symmetric with respect to
Odd Functions
the y CKIS
the Odd functions are symmetric with respect to
This means we could fold the graph on
the axis, and it would line up perfectly
This means we can flip Rotate the image 180°
on both sides!
and it will appear exactly
the same!
If we cannot classify whether a function as even or odd, then
Determine graphically the following functions are even, we odd, call it neither!
Even
or
1. Niether
neither.
2.
10
Even.
10
8
3.
8
4
6
exect
2
6
4
4
same
2
2
thing
de
4
5
symmetre
-8
10
8
-12
-10
4. odd
our
yaks
10
5.
10
8
6. Neither 10
8
E
8
6
4
6
4
2
4
2
-2
4
-2
6
s
6
-10
8
1-10
To verify algebraically if a function is even, odd, or neither, we must prove(one of the following
For even prove:
fl-x)=f(x)
For odd prove: f(-x):-f(x)
If neither of the above are true, we call the function neither!
Function
What to do
Example.
Notation
f(x) = x 2 - 3 x + 5
f(x)
Repeat the original function.
f(x) = x 2 - 3 x + 5
f(-x)
Plug in a (-x) for
every
X and simplify!
f(x) = x 2 - 3x + 5
-f(x)
Multiply every term in f(x)
by a -1.
neither
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