Question

use translations to graph the given function.
$m(x)=|x - 4|$

Explanation:

Step1: Identify parent function

The parent function is $f(x) = |x|$, which has a V-shape with vertex at $(0,0)$, passing through $(-1,1)$ and $(1,1)$.

Step2: Determine translation rule

For $m(x)=|x-4|$, the form $|x-h|$ shifts $f(x)$ right by $h$ units. Here $h=4$, so shift right 4 units.

Step3: Find key points of $m(x)$

• Vertex of $f(x)$: $(0,0)$ → shifted to $(0+4, 0)=(4,0)$
• Point $(-1,1)$ of $f(x)$ → shifted to $(-1+4,1)=(3,1)$
• Point $(1,1)$ of $f(x)$ → shifted to $(1+4,1)=(5,1)$
• Additional points: $(2,2)$ and $(6,2)$ (from $|2-4|=2$, $|6-4|=2$)

Step4: Plot and connect points

Plot $(4,0)$, $(3,1)$, $(5,1)$, $(2,2)$, $(6,2)$, then draw the V-shaped graph through these points.

Answer:

The graph of $m(x)=|x-4|$ is a V-shaped graph with vertex at $(4,0)$, passing through points such as $(3,1)$, $(5,1)$, $(2,2)$, and $(6,2)$, formed by shifting the parent absolute value function $f(x)=|x|$ 4 units to the right.