GRAPHING POLYNOMIAL FUNCTIONS by iV0ZpZ

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									GRAPHING POLYNOMIAL FUNCTIONS

Graph each function on your graphing calculator, and then sketch the graph on this sheet.

(1) Cubic         Window: x: [-4.7, 4.7], y: [-10, 10]
a. f(x)  x3                  b. g(x)  x3               c. f(x)  x3  x2  5x  2    d. g(x)  x3  x2  5x  2




(2) Quartic             a. f(x)  x4  x3  7x2  x  6                       b. g(x)  x4  x3  7x2  x  6

 Window
 x: [-4.7, 4.7]
 y: [-10, 10]




(3) Quintic             a. f(x)  x5  x4  13x3  13x2  36x  36            b. g(x)  x5  x4  13x3  13x2  36x  36

 Window
 x: [-4.7, 4.7]
 y: [-60, 60]




(4) Sixth-degree a. f(x)  2x6  7x5  7x4  35x3  7x2  28x  12                 b. g(x) = -f(x)


  Window
  x: [-4.7, 4.7]
  y: [-100, 100]




_________________________________________________________________________________
(5) Double roots a. f(x)  (x  2)2 (x  1)       b. g(x)  (x  2)2 (x  1)

     Window
     x: [-4.7, 4.7]
     y: [-10, 10]
(5) Double roots
                     a. f(x)  (x  2)2 (x  1)(x  3)            b. g(x)  (x  2)2 (x  1)(x  3)
    Window
    x: [-4.7, 4.7]
    y: [-30, 30]




(6) Triple Roots     a. f(x)  (x  3)(x  1)3                    b. g(x)  (x  3)(x  1)3


   Window
   x: [-4.7, 4.7]
   y: [-30, 30]




_________________________________________________________________________________
Ex. (No calculator) Fill in the blanks, and sketch the graph. Ex. Use the given graph to fill in the blanks.
                        2
 f(x)   (x  2)(x  1) (x  3)
                                                                                y

Degree = ______       y-int. = _____

Roots = ________________________
                                                                                                  x
Sign of leading coefficient = _____




                                                             f is increasing on ________________

                                                             f is decreasing on ________________

                                                             Relative max. at ______________

                                                             Relative min. at ______________

                                                             f is concave up on _________________

                                                             f is concave down on _________________

                                                              Inflection points at __________________

								
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