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 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 key - point of parent function

The vertex of the parent function $f(x)=|x|$ is at the origin $(0,0)$.

Step3: Find vertex of translated function

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

Answer:

The graph where the vertex of the solid - line (representing $g(x)$) is at the point $(0,-4)$ (the first graph from the left where the V - shaped solid line has its lowest point at $y = - 4$ on the y - axis).