CA_GPS_33 - x-axis[Hint pick a point between the zeros Step...

Rev. S08 http://faculty.valenciacc.edu/ashaw/
COLLEGE ALGEBRA
NAME: ________________________________
GPS # 33 4.1 POLYNOMIAL FUNCTIONS Class Time: ____________ Date: __________
Useful Guidelines:
To Graph a Polynomial function,
0 1
1
1
... ) ( a x a x a x a x f
n
n
n
n
+ + + + =
!
!
, 0 !
n
a
* Step 1: Find the x -intercepts, if any (by solving the equation 0 ) ( = x f ), and the y -intercepts, ) 0 ( f .
* Step 2: Determine whether the graph crosses (when r is a zero of odd multiplicity)
or touches (when r is a zero of even multiplicity) the x -axis at each x -intercepts.
* Step 3: Check the end behavior: For large x , the graph of f behaves like the graph of
n
n
x a x f = ) ( .
* Step 4: Determine the degree of f = n and the maximum number of turning points on the graph of f = n -1 .
* Step 5: Use the x -intercept(s) to find the intervals on which f is above the x -axis and the intervals on which f
is above the