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|…

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) =

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) =

Answer

Explanation:

Step1: Recall translation rule

For a function $y = f(x)$, a translation $h$ units to the right gives $y=f(x - h)$. Here $f(x)=\vert x\vert$ and $h = 5$.

Step2: Apply the rule

Substitute $x$ with $x - 5$ in $f(x)$. So $g(x)=\vert x-5\vert$, which is in the form $a\vert x - h\vert + k$ with $a = 1$, $h=5$ and $k = 0$.

Answer:

$|x - 5|$