Is this function even, odd or neither?

Question

f(x) = 2x^2 + 3x and how do u knw wat it is?? thanks for the help

Answer 1

well, geometrically, any even function is one that is symmetric with respect to the y-axis, so the way we test for this symmetry is by replacing x with -x, then simplify, if the resulting equation is the same as the original the function is even. In this case, if we replace x with -x we get a different function which means it is not even.

if we replace both f(x) with -f(x) and x with -x to test for symmetry with respect to the origin, we also get a different answer, therefore the function is neither even nor odd

Answer 2

Well, it's a quadratic so it can't be Odd.

The question is whether it reaches a minimum/maximum at x=0, and since it has a non-zero x-term, I'd say that's not the case (turning point = -b/2a, which is non-zero in this case). So f(-x) is NOT = f(x), which means it's not even either.

So, I'd say it was neither even nor odd.

Answer 3

f(-1) = 2(-1)(-1) + 3(-1) = 2 - 3 = -1
f(1) = 2(1)(1) + 3 (1) = 2 + 3 = 5

A function is even if f(-x) = f(x). Does f(-1) = f(1)?

A function is odd if f(-x) = -f(x). Does f(-1) = - f(1)?