Question

graph the following function by translating ( y = |x| ).
( y = |x + 5| )

which graph below is the correct graph of ( y = |x + 5| )?

a.

b.

c.

d.

Explanation:

Step1: Recall absolute value shift rule

For $y=|x-h|$, shift $y=|x|$ right by $h$. For $y=|x+h|=|x-(-h)|$, shift left by $h$.

Step2: Identify shift for $y=|x+5|$

Here $h=5$, so shift $y=|x|$ left 5 units. The vertex of $y=|x|$ is $(0,0)$; new vertex is $(-5,0)$.

Step3: Match vertex to options

Find graph with vertex at $(-5,0)$, maintaining V-shape of $y=|x|$.

Answer:

B. <Graph with vertex at (-5, 0), opening upwards in a V-shape>