GrAssign - Poly Inequalities 

The above graph...

                1.  holds the solution to the inequality.

                2.  contains the zeros of the function.

                3.  is the graph of the actual function, f(x).  

The red copy should be recorded on the provided answer sheet.

    A.  Determine the zeros of the function.

          List all zeros of this function:  x =? x = ?,...

    B. Use the zeros to determine the factors of the function.

          Record the zeros as x = ?, then write as an ordered pair.

          1.  If x = ?, then the factor must be (write as an ordered pair).

          2.  If x = ?, then the factor must be (write as an ordered pair).

          3.  If x = ?, then the factor must be (write as an ordered pair).

          4.  If x = ?, then the factor must be (write as an ordered pair).

   C. Define the function.

           Using the ordered pairs, define the function f(x).  Do not multiply the factors.  

           f(x) = ?

   D. Determine the behavior of the function around the zeros.

        If we look at the blue regions and the function's graph, that is,

           its actual behavior, we can graph the results on a number line.

          Before that, let's look at how the regions are enclosed. 

Record the correct response(s) on the answer sheet.

      1.   The line is dashed/not dashed,  which means the inequality does/doesn't include the "equal to" sign.  

    2.  The zeros are/are not included, and we would use parentheses/brackets.

    3.    Region I - Blue/White region and the graph is below/above the x-axis  --> 

                             positive/negative on what interval?

     4.   Region II - Blue/White region and the graph is below/above the x-axis  --> 

                             positive/negative on what interval?

     5.  Region III - Blue/White region and the graph is below/above the x-axis  -->   

                             positive/negative on what interval?

     6.  Region IV - Blue/White region and the graph is below/above the x-axis   -->  

                             positive/negative on what interval?

     7.   Region V - Blue/White region and the graph is below/above the x-axis   -->  

                             positive/negative on what interval?

      E.  Number line graph - include the zeros.

          Include all zeros, test points, and the behavior on the answer sheet.

       <~~~~~~~~~~~~(?)~~~~~~~~~~(?)~~~~~~~~~~~~~(?) ~~~~~~~~~~~~~~(?)~~~~~~~~~~~>

     F. Determine the solution set for the polynomial inequality  

        If we are looking at the blue region, the solution is all values of x that would result in the function's value less than/greater than 0

          1.  Use interval notation to identify the solution set for the blue regions:          

       2.  Write the polynomial inequality. Don't multiply the factors.