Question

select one: a. $f(x) = -|x - 1| - 4$ b. $f(x) = -|x + 1| - 4$ c. $f(x) = -|x - 1| + 4$ d. $f(x) = -|x + 1| + 4$

Explanation:

Step1: Recall vertex form of absolute value function

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

Step2: Identify vertex from the graph

From the graph, the vertex (the highest point) is at $(1, 4)$, so $h=1$, $k=4$. The graph opens downward, so $a=-1$.

Step3: Substitute values into vertex form

Substitute $a=-1$, $h=1$, $k=4$ into the vertex form:
$f(x) = -|x - 1| + 4$

Step4: Match with given options

This matches option C.

Answer:

C. $f(x) = -|x - 1| + 4$