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

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.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square