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

Answer:

The first graph.

Explanation:

Step1: Recall translation rule

For a function $y = f(x)+k$, if $k<0$, the graph of $y = f(x)$ is shifted down by $|k|$ units. Here $g(x)=|x|- 4=f(x)-4$, so the graph of $f(x) = |x|$ is shifted down 4 units.

Step2: Analyze graphs

The parent - function $f(x)=|x|$ has its vertex at the origin $(0,0)$. The function $g(x)=|x|-4$ has its vertex at $(0, - 4)$. The first graph shows the dashed line $y = |x|$ (parent - function) and the solid line $y=|x|-4$ which is shifted down 4 units from the parent - function.