graph the equation shown below by transforming the given graph of the parent function. y = |x - 4|

Explanation:

Step1: Identify parent - function

The parent function of $y = |x - 4|$ is $y=|x|$. The graph of $y = |x|$ has a V - shape with the vertex at the origin $(0,0)$.

Step2: Apply horizontal - shift rule

For a function of the form $y = f(x - h)$, the graph of $y = f(x)$ is shifted $h$ units to the right. In the function $y=|x - 4|$, $h = 4$. So, the graph of $y = |x|$ is shifted 4 units to the right. The vertex of $y = |x - 4|$ is at the point $(4,0)$.

Step3: Plot key points

For $y = |x - 4|$, when $x=4$, $y = 0$; when $x=5$, $y=|5 - 4|=1$; when $x = 3$, $y=|3 - 4| = 1$. Plot these points and draw the V - shaped graph with the vertex at $(4,0)$.

Answer:

The graph of $y = |x - 4|$ is the graph of the parent function $y = |x|$ shifted 4 units to the right with the vertex at the point $(4,0)$.