3.1_Exploring.Polynomials_student - st differences are...

MHF 4U0
3.1 Exploring Polynomial Functions
A polynomial function is a function that has the form f(x) = a
n
x n + a
n–1
x n–1 + … + a
2
x 2 + a
1
x + a
o
,
where:
• a
n
, a
n-1
, … are real numbers
• n is a positive integer ( n is called the degree of the polynomial)
Example #1:
Which of the following functions are polynomials? State the degree for each polynomial.
Function Polynomial?
(Yes/No)
Degree
4 2 3 ) (
2
- + = x x x f
2 6
4 ) ( x x x g + - =
2
) (
-
= x x h
x
x x k
1
) (
3
+ =
1 3 ) ( - = x x m
x x p = ) (
x
x q 4 ) ( =
9
6 3 1000 ) ( x x x r + - =
SUMMARY:
• The domain of a polynomial function is the set of all real numbers.
• The range of a polynomial function may be all real numbers, or it may have a lower bound
or an upper bound (but not both).
• The graphs of polynomial functions do not have horizontal or vertical asymptotes.
• The n th finite differences of a polynomial function of degree n are constant.
o Linear functions => 1