Question

select the correct answer.
consider the function graphed below.
if f is translated 4 units down to create g, which function represents g?
a. g(x) = f(x + 4)
b. g(x) = f(x) + 4
c. g(x) = f(x - 4)
d. g(x) = f(x) - 4

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( y = f(x) \), a vertical translation down by \( k \) units (where \( k>0 \)) is given by \( y = f(x)-k \).

Step2: Apply the Rule to the Problem

Here, the translation is 4 units down. So using the vertical translation rule, if \( f \) is translated 4 units down to get \( g \), then \( g(x)=f(x) - 4 \). We can eliminate options A and C (which are horizontal translations) and option B (which is a vertical translation up).

Answer:

D. \( g(x) = f(x) - 4 \)