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.

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

Step-by-step 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.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.