| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

View
 

Polynomial-Functions-of-a-Higher-Degree

Page history last edited by Kristen Fouss 15 years, 2 months ago

 

 2.2 Polynomial Functions

of a Higher Degree

 

What exactly is a polynomial function..and what does it's graph look like?

 

Polynomial functions are functions that have this form:

 

f(x) = anxn + an-1xn-1 + ... + a1x + a0

 

 

Polynomial Functions In An Exaggerated 3D Motif

 A Polynomial function's graph is continuous. This means that the graph has no breaks, holes, gaps or sharp turns.

*as shown below 

                   Odd degree function (p7.gif)

Function w/ EVEN power                                 Function w/ ODD power

 

*As the power "n" goes up, the flatter or skinnier the graph gets 

     *these graphs would both become skinnier as the "n" power went up

          * the "n" in the equation represents the exponent

 

even polynomial fns. graphs are always similar to f(x)= x^2

*but, the higher the exponent, the skinnier the graph gets 

EXAMPLE-  x^6 is similiar to x^4: the only difference would be the thickness of the graph and possibly a shift in the graph due to other variables and exponents

x^4 compared to x^6

  Graph

 

odd polynomial fns. graphs resemble f(x)= x^3

*this also gets skinnier as the exponent becomes bigger

EXAMPLE-  x^5 is similiar to x^3: the only difference would be the thickness of the graph and possibly a shift in the graph due to other variables and exponents 

x^3 compared to x^5

Graph 

*If there is a negative before the biggest exponent; the graph flips and is the opposite of the positive 

 

END BEHAVIORS:

for x^2;  x goes to -infinity as y goes to infinity AND x goes to infinity as y goes to infinity

for -x^2; x goes to -infinity as y goes to -infinity AND x goes to infinity as y goes to -infinity

for x^3; x goes to -infinity as y goes to infinity AND x goes to infinity as y goes to infinity

for -x^3; x goes to -infinity as y goes to infinity AND x goes to infinity as y goes to - infinity

 

*this is basically the domain of the polynomial functions

     *the relationships between the X and Y as they go along the continuous line

 

Even and odd polynomial fns. graphs  *good sites for extra review

 

http://rechneronline.de/function-graphs/

 

http://cnx.org/content/m15241/latest/

 

http://id.mind.net/~zona/mmts/functionInstitute/polynomialFunctions/polynomialFunctions.html 

 

POLYNOMIAL OF HIGHER DEGREES VIDEOS

  

*video created by the St. Petersburg College established in 1927

Chapter 2.2 - Polynomial Functions of Higher Degree Chapter 2.2 - Polynomial Functions of Higher Degree
Chapter 2.2 "Polynomial and Rational Functions" - Polynomial Functions of Higher Degree
 
31 minutes

 

Comments (0)

You don't have permission to comment on this page.