Question

For a given function ƒ(x) = x5, a translation in the positive y-direction of two units is represented by which of the following?

Question 5 options:

A)

ƒ(x + 2) = ( x – 2)5

B)

ƒ(x + 2) = (x + 2)5

C)

ƒ(x) – 2 = x5 – 2

D)

ƒ(x) + 2 = x5 + 2

Answer 1

D) ƒ(x) + 2 = x5 + 2

Explanation:

You have the following function:

`f(x)=x^5` (1)

In the case of a vertical translation of the function on the coordinate system, you have that a translation of a units upward is obtained with the function f(x)+a. In the same way, a translation downward is obtined with f(x)-a.

Thus, a translation in the positive y direction of 2 units (a=2) is given by the following function.

D) ƒ(x) + 2 = x5 + 2