Question

which of the following is the graph of this absolute value function?
$y = |x| + 1$

Explanation:

Step1: Identify parent function

The parent function is $y=|x|$, which has a vertex at $(0,0)$, opens upward, and has a V-shape.

Step2: Analyze vertical transformation

The given function is $y=|x|+1$, which is a vertical shift of the parent function up by 1 unit. This moves the vertex to $(0,1)$.

Step3: Verify key points

• When $x=0$, $y=|0|+1=1$, so vertex is $(0,1)$.
• When $x=2$, $y=|2|+1=3$; when $x=-2$, $y=|-2|+1=3$. These points $(2,3)$ and $(-2,3)$ lie on the graph.

Answer:

The third graph (with vertex at $(0,1)$, passing through $(-2,3)$ and $(2,3)$) is the correct graph of $y=|x|+1$.