Question

Determine algebraically whether the function g(x)=x^2 is even odd or neither

Answer 1

I think its 2 because its 2 so you will put 2

Answer 2

g(x) = x^2

g(-x) = (-x)^2 ... replace every x with -x

g(-x) = x^2 ... squaring a negative makes it positive

So because g(x) = g(-x) for every x, this means g(x) is an even function. For polynomials, if every exponent is even, then the entire polynomial is even as well.

Note: if a function is even, then it won't be odd or vice versa unless the function is the zero function. In other words, g(x) = 0 is both even and odd.