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