Question

graph the function:
$f(x) = -|2x + 3| + 6$
(there are four graphs with options, and at the bottom its labeled question 15)

Explanation:

Step1: Identify vertex 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. Rewrite the given function:
$f(x)=-1|x-(-3)|-6$
So the vertex is $(-3, -6)$.

Step2: Find slope for two branches

For $x > -3$, $f(x)=-1(x+3)-6 = -x-9$, slope $=-1$.
For $x < -3$, $f(x)=-1(-x-3)-6 = x-3$, slope $=1$.

Step3: Match to correct graph

Locate the graph with vertex at $(-3, -6)$, left branch with slope 1, right branch with slope -1.

Answer:

The correct graph is the fourth (bottom-most) graph with vertex at $(-3, -6)$, rising to the left and falling to the right.