determine if this function is odd, even or NEITHER

Question

is 2x^7-x^3+2 an even, odd or neither function?

Answer 1

Substitute -x for x.

2(-x)⁷ - (-x)³ + 2

Two negative numbers multiply to a positive product, right? With odd exponents, a negative base stays negative.

(-5)⁵ = (-5)(-5)(-5)(-5)(-5) = -3125

So, we end up with -2x⁷ + x³ + 2

That's not the original function, and the last sign (+2) didn't change, so it's NEITHER.

Answer 2