5.1C  Determining the Behavior of a Function

Determining the Behavior of a Function 

     In the previous lesson, you learned how to find the solution set to a quadratic inequality. 

    We will use that process to graph all quadratic functions without and with a grapher.

Problem 1 

   The problem below asks you to find the function's behavior. (Problem from the last lesson). 

   To understand the process, work through this example (don't just read it, do the math)

         Given 9(x - 4) - x2(x - 4) = 0, determine the function's behavior around its zeros.

              We determined the zeros:   x = -3, x = 3, x = 4.

              We used test points to determine the behavior around these test points.

            pos                   neg                  pos             neg            Behavior                                                                                             of  f(x)

      <-------------(-3) -------------(3)-----------(4)---------->       Zeros

             -4                      0                    3.5               5          Test points

   Because this is an equation, notice the equal and not less than, we will now determine the behavior of the function around the zeros, so we can sketch a rough graph of the function without using the grapher.  Let's look at the diagram below.  Pay close attention to the blue text ->  Behavior of f(x)