Question

what kind of transformation converts the graph of $f(x) = -7|x - 4|$ into the graph of $g(x) = -7|x - 4| + 2$?
translation 2 units down
translation 2 units right
translation 2 units left
translation 2 units up

Explanation:

Step1: Recall vertical translation rule

For a function \( y = f(x) \), the transformation \( y = f(x)+k \) represents a vertical translation. If \( k>0 \), it is a translation \( k \) units up; if \( k < 0 \), it is a translation \( |k| \) units down.

Step2: Compare \( f(x) \) and \( g(x) \)

Given \( f(x)=-7|x - 4| \) and \( g(x)=-7|x - 4|+2 \). Here, we can think of \( g(x)=f(x)+2 \). By the vertical translation rule, since \( k = 2>0 \), this is a translation 2 units up.

Answer:

translation 2 units up