Reversing the Process - Rational Inequalities

Again, we will work backward -

        We will study a graph (rather than a function)

      to determine the function (rather than what the graph might look like).

        Below is a graph with some highlighted key points,

       so we will begin by analyzing the graph to determine:

          ~  Zeros of the function

          ~  Factors of the function

          ~  Vertical asymptote (if any)

          ~  Negative and positive regions

          ~  The rational function

          ~  The number line with the zeros and +/- regions

          ~  The rational inequality

          ~   Solution Set

Example 10:  Graphically 

    Let's assume the green area contains the solution set.
    We will now analyze the graph to answer the questions noted above.