Question

find g(x), where g(x) is the translation 5 units right of f(x) = |x|. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) =

Explanation:

Step1: Recall translation rules

For a function \( y = f(x) \), translating it \( h \) units right gives \( y = f(x - h) \), and translating \( k \) units up gives \( y = f(x)+k \). The vertical stretch factor is \( a \).
For \( f(x)=|x| \), we have \( a = 1 \) (no vertical stretch), \( k = 0 \) (no vertical translation), and we translate 5 units right, so \( h = 5 \).

Step2: Apply the translation

Using the form \( g(x)=a|x - h|+k \), substitute \( a = 1 \), \( h = 5 \), and \( k = 0 \) into the formula.
We get \( g(x)=1|x - 5|+0 \), which simplifies to \( g(x)=|x - 5| \).

Answer:

\( |x - 5| \)