Question

which of the following functions is graphed below? a. $y = |x - 3| - 4$ b. $y = |x - 3| + 4$ c. $y = |x + 3| - 4$ d. $y = |x + 3| + 4$

Explanation:

Step1: Identify vertex of absolute value graph

The vertex (lowest point) of the graphed absolute value function is at $(-3, -4)$.

Step2: Recall absolute value vertex form

The vertex form of an absolute value function is $y = |x - h| + k$, where $(h,k)$ is the vertex.

Step3: Substitute vertex values

Substitute $h = -3$ and $k = -4$ into the vertex form:
$y = |x - (-3)| + (-4) = |x + 3| - 4$

Step4: Match to options

This matches option C.

Answer:

C. $y = |x + 3| - 4$