Question

Which characteristic is correct for the function f(x) = −2x^3 + 3x^2 ?

A. even

B. neither even nor odd

C. odd

D.both even and odd

Answer 1

The answer is B because if you add the negative sign it will change

Answer 2

B

Explanation:

The function is cubic (the highest power is 3), so it can't be even. It's either odd or neither.

We can either graph the function, or we can test that it's symmetrical about the origin by seeing if f(x) = -f(-x).

f(x) = -2x³ + 3x²

f(-x) = -2(-x)³ + 3(-x)²

f(-x) = 2x³ + 3x²

f(x) ≠ -f(-x), so the function is neither even nor odd.