Name ________________________ Date _______________ Period ________
Pre-Calculus: Section 4.1 Polynomial Functions and Models
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
Polynomial
Function
Constant
Linear
Quadratic
Cubic
Quartic
Fill in the following table to describe five classes of Polynomial Functions:
Example
General
Shape
Degree
(Highest Power)
Leading
Term
Leading
Coefficient
(Term containing
the Highest Power)
(Number portion of
the Leading Term)

Degree
End Behavior of a Function – The behavior of the “ends” of a graph. Basically
this tells what the “y” values are doing as the “x” values approach positive or
negative infinity. The degree and the leading coefficient of a polynomial
function determine the end behavior of the graph. (Remember that f(x) is the
same thing as y.)
Leading
Coefficient
End behavior of the function
Graph of the function
Example: f (x) = x2
Even
Positive
Example: f (x) = –x2
Even
Negative
Example: f (x) = x3
Odd
Positive
Example: f (x) = –x3
Odd
Negative

Zero’s of a Function – The x-vales that make the y-values equal to zero. These
are places the graph touches the x-axis and can be given by coordinates in the
form of (x, 0).

Multiplicity – When a factor has an even power, then the zero does not cross
the x-axis, but bounces off of it at that value. When a factor has an odd power,
then the zero crosses (intersects) the x-axis at that value.
o Ex. Use substitution to determine whether 2, 3, and -1 are zeros of the
function, g(x) = x4 – 6x3 + 8x2 + 6x - 9.
o Ex. Find the zeros of the following function and determine the
multiplicity:

f(x) = (x2 – 4)2

f(x) = -8(x – 3)2(x + 4)3x4

g(x) = x4 – 4x2 + 3

h(x) = x3 – x2 – 2x + 2