Question

The function h(x) = 12x + 49 is an even function. Which transformation of h(x) would result in a function that is neither

even nor odd?

Answer 1

A reflection over x - axis

Explanation:

If f(-x) = f (x), (ie all the signs are the same), then the function is even

also, if f(-x) = -f (x), (ie all the signs are switched), then the function is odd.

Given;

h(x) = 12x + 49

Then test for h(-x);

h(-x) = 12(-x) + 49

h(-x) = -12x + 49,

Thus h(-x) ≠ h(x) and also h(-x) ≠ -h(x)

The function is neither odd nor even.

Therefore, a reflection over x - axis would result in a function that is neither even nor odd.