Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = 5x^2 - 2

Answer 1

The function f(x) is even if:
f(-x) = f(x)

f(x) is odd if:
f(-x) = -f(x)

Plug in -x into f(x):
f(-x) = 5(-x)^2 - 2
f(-x) = 5x^2 - 2

We got back our original f(x) by plugging in -x, so f(-x) = f(x), and therefore the function is even.