Question

consider this graph.
replace h and k with the correct values to write the function that represents the given graph.

Explanation:

Step1: Identify vertex of the graph

The vertex (lowest point) of the absolute value graph is at $(-4, -1)$. For the vertex form of an absolute value function $y = |x - h| + k$, the vertex is $(h, k)$.

Step2: Match vertex to vertex form

From the vertex $(-4, -1)$, we get $h = -4$ and $k = -1$.

Step3: Confirm slope and function

The slope of the right segment is 1, so the coefficient of the absolute value term is 1. Substitute $h$ and $k$ into the vertex form:
$y = |x - (-4)| + (-1) = |x + 4| - 1$

Answer:

The function is $\boldsymbol{y = |x + 4| - 1}$, where $h = -4$ and $k = -1$.