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Polynomial Functions

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by

Juan Jorrin

on 5 March 2017

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Transcript of Polynomial Functions

Polynomial Functions
Polynomial in One Variable
A polynomial function is a function of the form
Find Degree and
Leading Coefficients
Polynomial Function
It represents the function of a polynomial equation.
Functional Values
of Variables
Graphs of Polynomial Functions
End Behavior of a Polynomial Function
Graphs of Polynomial Functions
Example: Polynomial in one variable
It contains only one variable, x.
The degree of the polynomial is the degree of the leading term.
The a are real numbers and are called coefficients.
n
Yes
The degree is 4 and the leading coefficient is 6.
No
It contains two variables, x and y.
No
The term 2/x cannot be written in the form
x , where n is a nonnegative integer.
n
Yes
Rewrite the expression according to the degree of exponents,
Examples:
quadratic polynomial
function
cubic polynomial
function
Evaluate a
Polynomial Function
Replace x with 3.
Simplify.
Replace x with -3.
Simplify.
Original function
Replace x with y .
2
Property of powers
To evaluate h(k + 1), replace y in h(y) with k + 1.
To evaluate 2h(y), replace y with k in h(y), then multiply the expression by 2.
Now evaluate h(k + 1) - 2h(k).
Constant function
Degree 0
Linear function
Degree 1
Quadratic function
Degree 2
Cubic function
Degree 3
Quartic function
Degree 4
Quintic function
Degree 5
Degree: even
Leading Coefficient: positive
End Behavior:
Degree: odd
Leading Coefficient: positive
End Behavior:
End Behavior of a Polynomial Function
Degree: even
Leading Coefficient: negative
End Behavior:
Degree: odd
Leading Coefficient: negative
End Behavior:
It is an even-degree polynomial function.
The graph intersects the x-axis at two points, so the function has two real zeros.
It is an odd-degree polynomial function.
The graph has one real zero.
The term a is assumed to be non-zero and is called the leading coefficient.
n
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