AP precalc 1.5 and 1.4

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