Given:
The graph of a function f(x).
To find:
The solution set for f(x)>0 and f(x)≤0.
Solution:
From the given graph it is clear that, the function intersect the x-axis at 3 points, i.e., x=-4, -3 and -2.
The graph is above the x-axis before -4 and between -3 and -2.
So, the solution set for f(x)>0 is [tex](-\infty,-4)\cup (-3,-2)[/tex].
The graph is below the x-axis between -4 and -3; and after -2. For f(x)≤0, those values are in the solution set for which f(x)=0, i.e., x-intercepts. So, we use close brackets in the interval notation.
So, solution set for f(x)≤0 is [tex][-4,-3]\cup [-2,\infty)[/tex].
