Question

the graph shows the function $f(x) = |x - h| + k$. what is the value of $h$? $\bigcirc$ $h = -3.5$ $\bigcirc$ $h = -1.5$ $\bigcirc$ $h = 1.5$ $\bigcirc$ $h = 3.5$

Explanation:

Step1: Recall vertex form of absolute function

The function \( f(x) = |x - h| + k \) has its vertex at \( (h, k) \). So we need to find the vertex of the given absolute - value graph.

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the point where the graph changes direction) is at \( x=-1.5 \) (since the x - coordinate of the vertex is \( h \) in the function \( f(x)=|x - h|+k \)). Let's confirm: The vertex is the minimum point of the V - shaped graph. From the grid, we can see that the vertex is at \( (-1.5,-3.5) \). In the function \( f(x)=|x - h|+k \), the x - coordinate of the vertex is \( h \). So if the vertex has an x - coordinate of \( - 1.5 \), then \( h=-1.5 \).

Answer:

\( h = - 1.5 \) (corresponding to the option: \( h=-1.5 \))