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?

A) reflection over the x-axis
B) vertical stretch by a factor of 7
C) translation 8 units to the right
D) horizontal compression

Explanation of the correct answer would be nice so that I understand it better.

Answer 1

Answer:

The correct option is;

C) Translation 8 units to the right

Step-by-step explanation:

The function h(x) = 12·x⁸ + 49 is an even function

However a translation 8 units to the right would yield the following function;

h(x) = 12 × (x+ 8)⁸ + 49 = 12x⁸ + 768x⁷ + 21504x⁶ + 344064x⁵ + 3440640x⁴ + 22020096x³ + 88080384x² + 201326592x + 201326641

For h(1) = 516560701

Also h(-x) = 12 × (-x+ 8)⁸ + 49 = 12x⁸ - 768x⁷ + 21504x⁶ - 344064x⁵ + 3440640x⁴ - 22020096x³ + 88080384x² - 201326592x + 201326641

For h(-1) = 69177661

Therefore h(x) ≠ h(-x) after the translation 8 units to the right and the function is neither even nor odd.