Question

which equation corresponds with the graph of the absolute value below? \\(\bigcirc\\ f(x)=2|x + 8|+4\\) \\(\bigcirc\\ f(x)=|x + 3|-4\\) \\(\bigcirc\\ f(x)=|x - 8|-4\\) \\(\bigcirc\\ f(x)=\frac{1}{2}|x - 2|-4\\)

Explanation:

Step1: Identify vertex form

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

Step2: Locate vertex from graph

From the graph, the vertex is at $(-3, -4)$. So $h=-3$, $k=-4$.

Step3: Determine slope $a$

The graph has a slope of $1$ on the right side of the vertex, so $a=1$.

Step4: Substitute values into form

Substitute $a=1$, $h=-3$, $k=-4$ into the vertex form:
$f(x)=1|x-(-3)|+(-4)=|x+3|-4$

Step5: Match with options

This matches the second option.

Answer:

B. $f(x) = |x + 3| - 4$