Question

which statement is true about the graphed function?
o f(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
o f(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
o f(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
o f(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).

Explanation:

Step1: Analyze the graph

We need to determine where \(y = f(x)>0\) (above the \(x -\)axis) and \(y = f(x)<0\) (below the \(x -\)axis).

Step2: Check intervals

• For the interval \((-\infty,- 0.7)\), the graph is above the \(x -\)axis, so \(f(x)>0\) in \((-\infty,-0.7)\).
• For the interval \((-0.7,0.76)\), the graph is below the \(x -\)axis, so \(f(x)<0\) in \((-0.7,0.76)\).
• For the interval \((0.76,2.5)\), the graph is above the \(x -\)axis, so \(f(x)>0\) in \((0.76,2.5)\).
• For the interval \((2.5,\infty)\), the graph is below the \(x -\)axis, so \(f(x)<0\) in \((2.5,\infty)\)

Answer:

\(f(x)<0\) over the intervals \((-\infty,-0.7)\) and \((0.76,2.5)\)