Question

which statement is true about the graphed function ( f(x) )?
( f(x)<0 ) over the intervals ( (-infty,-2.5) ) and ( (-0.75,0.75) ).
( f(x)>0 ) over the intervals ( (-infty,-2.5) ) and ( (-0.75,0.75) ).
( f(x)<0 ) over the intervals ( (-2.5,-0.75) ) and ( (-0.75,infty) ).
( f(x)>0 ) over the intervals ( (-2.5,-0.75) ) and ( (0.75,infty) ).

Explanation:

Step1: Analyze the graph

When \(y = f(x)>0\), the graph is above the \(x -\)axis. When \(y = f(x)<0\), the graph is below the \(x -\)axis.

Step2: Check each interval

• For the interval \((-\infty,-2.5)\): The graph is above the \(x -\)axis, so \(f(x)>0\)
• For the interval \((-2.5,-0.75)\): The graph is below the \(x -\)axis, so \(f(x)<0\)
• For the interval \((-0.75,0.75)\): The graph is above the \(x -\)axis, so \(f(x)>0\)
• For the interval \((0.75,\infty)\): The graph is below the \(x -\)axis, so \(f(x)<0\)

Answer:

\(F(x)>0\) over the intervals \((-\infty,-2.5)\) and \((-0.75,0.75)\) (the second option).