which statement is true about the graphed function ( f(x) )?\n( f(x)<0 ) over the intervals ( (-infty,-2.5)…

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

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

Answer

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).