Question

which statement is true about the graphed function?
○ f(x) < 0 over the interval (-∞, -4)
○ f(x) < 0 over the interval (-∞, -3)
○ f(x) > 0 over the interval (-∞, -3)
○ f(x) > 0 over the interval (-∞, -4)
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Explanation:

Step1: Analyze the graph

We need to check the sign of \(y = F(x)\) for different intervals. For \(x\in(-\infty,- 3)\), we observe the position of the graph with respect to the \(x -\)axis.

Step2: Determine the sign

If the graph is above the \(x -\)axis, \(F(x)>0\); if it is below the \(x -\)axis, \(F(x)<0\). For the interval \((-\infty,-3)\), the graph of \(y = F(x)\) is above the \(x -\)axis.

Answer:

\(F(x)>0\) over the interval \((-\infty,-3)\)