Question

use translations to graph the given function.
$n(x)=|x|-3$

Explanation:

Step1: Identify parent function

Parent function: $f(x) = |x|$

Step2: Analyze translation type

For $n(x)=|x|-3$, subtract 3 from $f(x)$: vertical shift down 3 units.

Step3: Shift parent graph vertices

Vertex of $f(x)$ is $(0,0)$. New vertex: $(0, 0-3)=(0,-3)$
Other key points:

• For $x=3$: $n(3)=|3|-3=0$, point $(3,0)$
• For $x=-3$: $n(-3)=|-3|-3=0$, point $(-3,0)$
• For $x=1$: $n(1)=|1|-3=-2$, point $(1,-2)$
• For $x=-1$: $n(-1)=|-1|-3=-2$, point $(-1,-2)$

Step4: Plot and connect points

Draw a V-shaped graph through the shifted points.

Answer:

The graph of $n(x)=|x|-3$ is the parent absolute value graph $y=|x|$ shifted vertically downward by 3 units, with vertex at $(0,-3)$, passing through points like $(-3,0)$, $(3,0)$, $(-1,-2)$, and $(1,-2)$.