5.2B  Solving Rational Functions Behavior

Graph of Rational Function - Example 2

   The graph of the rational function is attached below.  Compare the graph to the above analysis.

   Intervals 

       ~  (-∞, -2) region is positive, therefore, the graph is above the x-axis and "hugs" the vertical asymptote at x = -2. 

          Notice the graph does NOT cross the x-axis.  

       It "hugs" the horizontal asymptote y = 2.

      ~  (-2, ½) region is negative, therefore, the graph is below the x-axis and "hugs" the vertical asymptote, x = -2.

      ~  (½, ∞) region is positive, therefore, the graph is above the x-axis and "hugs" the horizontal asymptote at y = 2. 

          This graph will cross the x-axis because of the zero at x = ½.