FUNCTIONS

1
Symmetric about the y axis
FUNCTIONS
Symmetric about the origin
2
Even functions have y-axis Symmetry
8
7
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5
4
3
2
1
-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.
3
Odd functions have origin Symmetry
8
7
6
5
4
3
2
1
-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.
4
x-axis Symmetry
We wouldnt talk about a function with x-axis
symmetry because it wouldnt BE a function.
8
7
6
5
4
3
2
1
-2
-3
-4
-5
-6
-7
5
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
6
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
7
If a function is not even or odd we just say
neither (meaning neither even nor odd)
Determine if the following functions are even,
odd or neither.
Not the original and all terms didnt change
signs, so NEITHER.
Got f(x) back so EVEN.
8
Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au