Question

Which statement correctly describes the relationship between the graph of f (x) = 2x and the graph of g (x) = f (x) − 4?

A. The graph of g (x) is the graph of f (x) translated 4 units up.

B. The graph of g (x) is the graph of f (x) translated 4 units right.

C. The graph of g (x) is the graph of f (x) translated 4 units left.

D. The graph of g (x) is the graph of f (x) translated 4 units down.

Answer 1

D. The graph of g (x) is the graph of f (x) translated 4 units down.

Step-by-step explanation:

To show a translation left or right, we add or subtract a value to x before the function is applied. That is not what has happened to this function, therefore this was not a horizontal translation.

To show a translation up or down, we add or subtract a value at the end of a function. The function g(x) = f(x) - 4 subtracts 4 from the end of the function f(x); this means that the function has been translated down 4 units.