find g(x), where g(x) is the translation 8 units up of f(x) = |x|. write your answer in the form a|x - h| +…
find g(x), where g(x) is the translation 8 units up 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 vertical - translation rule
For a function $y = f(x)$, a vertical translation $c$ units up gives $y=f(x)+c$.
Step2: Apply the rule to $f(x)=|x|$
Here $c = 8$ and $f(x)=|x|$, so $g(x)=|x| + 8$. In the form $a|x - h|+k$, we have $a = 1$, $h = 0$, and $k = 8$, so $g(x)=1|x-0|+8$.
Answer:
$|x| + 8$