Question

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

Explanation:

Step1: Analyze the graph

Look at the \(y -\)values (outputs of \(F(x)\)) for different \(x -\)values in the given intervals.

Step2: Check the interval \((-\infty,-4)\)

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

Step3: Check the interval \((-\infty,-3)\)

The graph has parts below and above the \(x -\)axis in the interval \((-\infty,-3)\). So \(F(x)>0\) is not True for all \(x\in(-\infty,-3)\) and \(F(x)<0\) is not True for all \(x\in(-\infty,-3)\).

Step4: Check the interval \((-\infty,-4)\) again (for contrast with \((-\infty,-3)\))

Since the left - most part of the graph (for \(x < - 4\)) is above the \(x -\)axis, \(F(x)>0\) for \(x\in(-\infty,-4)\)

Answer:

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