which statement is true about the graphed function? f(x) < 0 over the interval (-∞, -4) f(x) < 0 over the…

Answer:

D. $F(x)>0$ over the interval $(-\infty, - 4)$

Explanation:

Step1: Analyze the graph

Observe the $y -$values of the function for different $x -$values.

Step2: Check $x\in(-\infty,-4)$

For $x$ values in the interval $(-\infty,-4)$, the graph of the function is above the $x -$axis. When a graph of a function $y = F(x)$ is above the $x -$axis, $y=F(x)>0$.

Step3: Check other intervals

For the interval $(-\infty,-3)$, the graph dips below the $x -$axis in the part of the interval $(-4,-3)$. So $F(x)<0$ for some $x$ in $(-\infty,-3)$ and $F(x)>0$ for $x\in(-\infty, - 4)$. So options A, B, and C are incorrect.