Question

How do you check for symmetry with respect to the origin and both axis x and y? The algebraic way please.

Answer 1

Even and odd functions?

Answer 2

Yes but I need to know what steps I can take to determine if it is an even function or an odd one.

Answer 3

OK, a function f(x) is even if f(-x)=f(x), a function f(x) is odd if f(-x)=-f(x).

Answer 4

An even function is symmetric about the y axis, an odd function is symmetric about the origin.

Answer 5

can you show me an example?

Answer 6

OK, lets see if f(x)=x^2 is even or odd, to find if its even we do this f(-x) = (-x)^2 which give us x^2. We see that x^2 is even.

Answer 7

And its graph is symmetric about the y axis