1. Symmetric about the y axis
FUNCTIONS
Symmetric about the origin

2. Even functions have y-axis Symmetry8 7 6 5 4 3 2 1 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 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.

3. Odd functions have origin Symmetry8 7 6 5 4 3 2 1 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 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.

4. x-axis Symmetry
We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function. 8 7 6 5 4 3 2 1 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 -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 didn’t 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.
Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar