Determine if the given functions are even, odd or neither. f (x) = - 2x2 - 7 and g (x) = 2x2 + 3

It's odd.

Explanation:

A function is odd when f (-x) = - f (x)

f (-x) = 6 (-x) 3 - 2 (-x)

=-6 x3 + 2x

= - (6 x3 - 2x)

= - f (x)

Thus, the function is odd.

If a function is odd, then it is symmetric over the x-axis.