use the graph of the function f to solve the inequality. (a) f(x)>0 (b) f(x)≤0 (a) the solution set for…

Explanation:

Step1: Analyze the graph for ( f(x)>0 )

We look at the regions where the graph of the function ( y = f(x) ) is above the ( x )-axis (( y>0 )). From the graph, we can see that the function ( y=f(x) ) is above the ( x )-axis when ( - 2<x<0 ).

Step2: Analyze the graph for ( f(x)\leq0 )

We look at the regions where the graph of the function ( y = f(x) ) is on or below the ( x )-axis (( y\leq0 )). The function ( y = f(x) ) is on or below the ( x )-axis when ( x<-2 ) or ( x\geq0 ).

Answer:

(a) The solution set for ( f(x)>0 ) is ( (-2,0) ). (b) The solution set for ( f(x)\leq0 ) is ( (-\infty,-2)\cup[0,\infty) ).