Are these functions odd, even or neither?

Question

f(x) = 2x – 15


f(x) = 42x2 + 14


f(x) = -5x + 3



f(x) = 3x3 – 5x



f(x) = 18x + 2

Answer 1

The second is even. The fourth is odd. The others are neither even nor odd

Answer 2

2x - 15: One term is always even and one is always odd.
42 * (anything) + 14: Both terms are always even.
-5x + 3: First term can be even or odd, second is always odd.
18x + 2: Both terms are always even.

So the answers on those four are odd, even, neither, and even.

For 3x^3 - 5x, the first term will be odd whenever the second one is and even whenever the second one is. Either way, the difference is even. So the function is even.