even and odd functions

EVEN:

an even function is when f(x) & f (-x) are equal. and they are symmetrical of the y-axis.

here is one example: f(x)= 3x^4+2x^2

well lets replace them and see...

f(-x)=3(-x)^4 + 2(-x)^2 simplifies to

= 3x^4 + 2x^2

and you then can determine that f(x) is in fact equal to f(-x).

plug in 1 and -1 one they will come out on the same horizontal line.

ODD:

now odd functions are different they are symmetrical about the origin. basically 180 degree turn.

however its the -f(x) is equal to f(-x)

example: f(x)= x^3-4x

f(-x)=(-x)^3 - 4(-x)

= -x^3 + 4x factor out the 1

= -(X^3 - 4X)

finally you can determine that f(-x) is equal to -f(x).

(note: i have not fully understood every concept to even and odd functions so,

i am accepting any type critique and/or comment pertaining to even and odd functions).

thanks.