Graphs of polynomial functions

Graphs of polynomial functions

• 2.
  The graph ofa polynomial function has the following characteristics  SMOOTH CURVE - the turning points are not sharp  CONTINUOUS CURVE – if you traced the graph with a pen, you would never have to lift the pen  The DOMAIN is the set of real numbers  The X – INTERCEPT is the abscissa of the point where the graph touches the x – axis.  ABSOLUTE MAXIMUM/MINIMUM is the highest or lowest point (respectively) of the graph of a polynomial function.  RELATIVE MAXIMUM/MINIMUM are the turning points of the graph of a polynomial function.
• 5.
  Value of Number of P(x) Degree leading Rational Number of turning (Odd/Even coefficient zeros x- points ) intercepts 1 Odd a >0 0 1 0 2 Odd a >0 2, 4, 6 3 2 3 Odd a< 0 4 1 2 4 Even a >0 0 1 1 5 Even a >0 1, -1, 2, -2 4 3 6 Even a< 0 none 0 1
• 6.
   How would you relate number of turning points with the degree of each function?  What can be said about the number of zeros that each graph has and its relationship with the degree of its respective function?  What seems to be true with the graph’s behavior and its degree? the value of its leading coefficient?
• 7.
   A polynomial function of degree n has  a maximum number of n-1 turning points  at most n x-intercepts
• 8.
  Leading Degree coefficient (Odd/Even) Description of the Graph a >0 Even Comes down from the left, goes up to the right a >0 Odd Comes up from the left, goes up to the right a< 0 Even Comes up from the left, goes down to the right a< 0 Odd Comes down from the left, goes down to the right
• 9.
  f ( x) x3
• 15.
   Describe the behavior of the following polynomial functions and identify the number of maximum zeros and turning points. 4 2 1. f ( x) x 13x 36 4 3 2 2. f ( x) 2x 2x 8x 8x 4 2 3. f ( x) x 13x 36