Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?

Question

A.
It is the graph of f(x) where the slope is decreased by 3.
B.
It is the graph of f(x) translated 3 units down.
C.
It is the graph of f(x) translated 3 units to the left.
D.
It is the graph of f(x) translated 3 units up.

Answer 1

The function \( g(x) = f(x) - 3 \) can be rewritten as \( g(x) = x - 3 \). This transformation indicates that the entire graph of \( f(x) = x \) is shifted down by 3 units.

Therefore, the correct statement that describes the graph of \( g(x) \) is:

B. It is the graph of f(x) translated 3 units down.