the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your…

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.

Answer

Explanation:

Step1: Identify the vertex of $g(x)$

The vertex of $f(x)=|x|$ is $(0,0)$. The vertex of $g(x)$ is at $(0, - 1)$.

Step2: Determine the values of $h$ and $k$

For the form $y = a|x - h|+k$, the $x$ - coordinate of the vertex gives $h$ and the $y$ - coordinate gives $k$. Here $h = 0$ and $k=-1$.

Step3: Determine the value of $a$

Since there is no vertical stretch or compression (the slope of the lines forming the absolute - value graph remains the same as that of $y = |x|$), $a = 1$.

Answer:

$g(x)=|x|-1$