Studied by 2 people
Fundamental theorem of algebra
Any polynomial function of x, with real number coefficients can be factored implement over the set of complex numbers
Conjugate root theorem
If p(x) is a polynomial with rational coefficients, then the irrational roots of p(x)=0 occur in conjugate pairs
Terms of symmetry
Even and odd
Even
A function f is even if and only if, when the point (x,y) is on the graph of f, then the point (-x,y) is also on the graph
F(-x)=f(x)
How to find the degree of a polynomial function from a table
The degree of the polynomial function is equal to the least value n for which successive nth differences are constant
Definition of polynomials
A monomial or the sun or monomials
A constant is a polynomial function of
Degree zero
If there exists an interval that contains b so that, for all x =/ in the interval
There is a local maximum or local minimum
Turning point
A point where the graph of a function changed direction form upwards to downwards of vice versa
End behavior
The direction of the graph as move to the left or to the right, away from the origin
E.B.M.
Local maximum
F has a local maximum at b when f(b) > f(x)
Local minimum
F has a local minimum at b when f(b) < f(x)
Absolute or global Extrema
The highest or lowest y-values on the graph of a function or on a specified domain of a function
Even degree polynomials
L.C > 0
Up
Unbounded
Even degree and L.C. < 0
Down down
Odd degree and L.C. > 0
Down up
Odd degree and L.C < 0
Up down
A point of inflection can occur at one of the three
At zero with a multiplicity of zero
Estimate a possible point of inflection between tow consecutive extreme values
Estimate a possible point of inflection between a zeros with multiplicity of three and the closest relative extreme value
