Question

graph the following function by translating ( y = |x| ).
( y = |x + 4| )

which graph below is the correct graph of ( y = |x + 4| )?

a.

b.

c.

d.

Explanation:

Step1: Recall parent function vertex

The parent function $y=|x|$ has vertex at $(0,0)$.

Step2: Identify horizontal translation rule

For $y=|x+h|$, shift left by $h$ units. Here $h=4$.

Step3: Calculate new vertex

New vertex: $(0-4, 0) = (-4, 0)$.

Step4: Match to option

Find graph with vertex at $(-4,0)$. Option A has this vertex.

Answer:

A. (Graph with vertex at (-4, 0))