Question

1. if $f(x)=|x + 4|-2$, write the function $g(x)$ that translates $f(x)$ 7 units right. a. $g(x)=|x - 3|-2$ b. $g(x)=-|x - 3|-2$ c. $g(x)=|x + 4|+11$ d. $g(x)=-|x + 4|+11$ e. $g(x)=7|x|$

Explanation:

Step1: Recall horizontal translation rule

For a function \( y = f(x) \), translating it \( h \) units to the right gives \( y = f(x - h) \). Here, \( h = 7 \) and \( f(x)=|x + 4|-2 \).

Step2: Apply the translation

Substitute \( x - 7 \) into \( f(x) \):
\( g(x)=f(x - 7)=|(x - 7)+4|-2 \)

Step3: Simplify the expression

Simplify the inside of the absolute value: \( (x - 7)+4=x - 3 \). So \( g(x)=|x - 3|-2 \).

Answer:

A. \( g(x)=|x - 3|-2 \)