on each coordinate plane, the parent function $f(x)=|x|$ is represented by a dashed line and a translation…

on each coordinate plane, the parent function $f(x)=|x|$ is represented by a dashed line and a translation is represented by a solid line. which graph represents the translation $g(x)=|x|-4$ as a solid line?

on each coordinate plane, the parent function $f(x)=|x|$ is represented by a dashed line and a translation is represented by a solid line. which graph represents the translation $g(x)=|x|-4$ as a solid line?

Answer

Explanation:

Step1: Recall vertical - translation rule

For a function $y = f(x)+k$, if $k\lt0$, the graph of $y = f(x)$ is translated $|k|$ units down. Here, $f(x)=|x|$ and $g(x)=|x|-4=f(x) - 4$, so the graph of $y = |x|$ is translated 4 units down.

Step2: Analyze the vertex of the parent - function and the translated function

The vertex of the parent function $y = |x|$ is at the point $(0,0)$. For the function $g(x)=|x|-4$, when $x = 0$, $y=-4$. So the vertex of $g(x)$ is at the point $(0, - 4)$.

Answer:

The graph where the vertex of the solid - line (graph of $g(x)$) is at the point $(0,-4)$ (the first graph from the left as the vertex of the solid V - shaped line is at $(0, - 4)$ while the vertex of the dashed line $y = |x|$ is at $(0,0)$)