Question

The function h(x)= 12x^8+49 is an even function. Which transformation of h(x) would result in a function that is neither even nor odd?

Answer 1

A translation (9 units) to the left will result in a function that is neither even nor odd

Explanation:

With horizontal translation to the left, we have;

h(x) = 12(x - 9)⁸ + 49

Which gives;

h(x) = 12(x - 9)⁸ + 49 = 12(x⁸ - 72x⁷ + 2268x⁶ - 40824x⁵ + 459270x⁴ -3306744x³ + 14880348x² - 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 201326641

When we replace x by -x, we get;

h(x) = 12(-x - 9)⁸ + 49 = 12(x⁸ + 72x⁷ + 2268x⁶ + 40824x⁵ + 459270x⁴ + 3306744x³ + 14880348x² + 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 1200000049

Therefore a translation 9 units to the left will result in a function that is neither even nor odd.