Substitute a -x for every x in the function. For example:
f(x) = x^2
f(-x) = (-x)^2
Simplify the new expression, and check to see whether it is the same as the original function. If it is, this is an even function and the graph is symmetric and you are finished. For example:
f(-x) = (-x)^2
f(-x) = x^2 = f(x)
This is an even function.
If the function was not even, write a negative sign in front of the original function. For example:
f(x) = x^3
f(-x) = (-x)^3 = -x^3
This is not an even function.
-f(x) = -(x^3)
Simplify the new expression, and check to see whether it is the same as the function with the substituted -x. If it is, this is an odd function and the graph is symmetric. If not, the graph is not symmetric. For example:
f(x) = x^3
f(-x) = (-x)^3 = -x^3
-f(x) = -(x^3) = -x^3
-f(x) = f(-x)
This is an odd function.