find g(x), where g(x) is the translation 2 units down of f(x) = |x|. write your answer in the form a|x - h|…

find g(x), where g(x) is the translation 2 units down 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 2 units down 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 $k$ units down is given by $y=f(x)-k$.

Step2: Identify the original function and $k$ value

The original function is $f(x)=|x|$ and $k = 2$ (since it is translated 2 units down).

Step3: Write the new function

Substitute $f(x)=|x|$ and $k = 2$ into the vertical - translation formula. So $g(x)=|x|- 2$, which can be written in the form $1|x - 0|+(-2)$ where $a = 1$, $h = 0$, and $k=-2$.

Answer:

$1|x - 0|+(-2)$ or simply $|x|-2$