Question

Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) - 13?

A) The graph of y = f(x) will shift up 13 units.
B) The graph of y = f(x) will shift right 13 units.
C) The graph of y = f(x) will shift left 13 units.
D) The graph of y = f(x) will shift down 13 units.​

Answer 1

Answer: D) The graph of y = f(x) will shift down 13 units.​

Explanation:

Let's define the transformations of translations.

If we start with a function f(x):

For A > 0.

An horizontal translation of A units to the right is written as g(x) = f(x - A)

An horizontal translation of A units to the right is written as g(x) = f(x + A).

A vertical translation of A units up is written as g(x) = f(x) + A

A vertical translation of A units down is written as g(x) = f(x) - A.

In this question we have the transformation:

y = f(x) - 13

This is a translation of 13 units down, then the correct option is:

D) The graph of y = f(x) will shift down 13 units.​