2.4 Polynomial and Rational Functions Flashcards
What is the definition of a Polynomial function?
What do the graphs of different degrees of Polynomials look like?
Characteristics of the odd-degreed polynomials
the odd-degree polynomial graphs start negative, end positive, and
cross the x axis at least once.
Characteristics of the even-degree polynomial
The even-degree polynomial graphs start positive, end positive, and may not cross the x axis at all.
What is the leading coefficent?
the leading coefficient—that is, the coefficient of the highest-degree term
How many liniar factors can a polynomial of degree n have?
A polynomial of degree n can have, at most, n linear factors.
How many times can a polynomial function of positive degree n intersect the x axis?
a polynomial function of positive degree n can intersect the x axis at most n times.
What are other names for an x intercept?
An x intercept of a function is also called a zero or root of the function.
Is the graph of a polynomial continuous?
The graph of a polynomial function is continuous, with no holes or breaks.
Are there sharp corners in the graph of a polynomial?
The graph of a polynomial has no sharp corners
Examples of graphs that are not polynomials
Definition of a rational function
How many vertical asymptotes are in a rational function?
The number of vertical asymptotes of a rational function f(x) =n(x)/d(x) is
at most equal to the degree of d(x).
How many horizontal asymptotes can a rational function have?
A rational function has at most one horizontal asymptote
What is the procedure for determining horzontal and vertical asymptotes of rational functions?
How do you get the difference of squares and the sum of cubes?
