PreCal Ch. 2 Vocab 11/11/10

quadratic, parabola

A ___________ function is a second-degree polynomial function, and its graph is called a ________.

n, n-1, relative extrema

A polynomial function of degree "n" has at most _____ real zeros and at most ________ turning points, called ____________.

upper bound, lower bound

A real number "b" is an ________________ for the real zeros of "f" if no zeros are greater than "b", and is a ______________ if no real zeros of "f" are less than "b".

quadratic

A scatter plot that appears parabolic can be better modeled by a ___________ equation.

linear

A scatter plot with either a positive or a negative correlation can be better modeled by a __________ equation.

synthetic division

An alternative method to long division of polynomials is called __________, in which the divisor must be of the form x - k.

real, imaginary

Complex numbers can be plotted in the complex plane, where the horizontal axis is the ________ axis and the vertical axis is the ___________ axis.

rational functions

Functions of the form f(x) = N(x) / D(x), where N(x) and D(x) are polynomials and D(x) is not the zero polynomial, are called _______________.

complex conjugate

If a + bi is a complex zero of a polynomial with real coefficients, then so is its ______________.

touches, crosses

If a zero of a polynomial funtion is of even multiplicity, then the graph of "f" __________ the x-axis, and if the zero is of odd multiplicity, then the graph of "f" ________ the x-axis.

vertical asymptote

If f(x) -> +/- infinity as x -> a from the left (or right), then x = a is a ______________ of the graph of "f".

horizontal asymptote

If f(x) -> b as x -> +/- infinity, then y = b is a ________________ of the graph of "f".

negative, maximum

If the graph of a quadratic function opens downward, then its leading coefficient is _________ and the vertex of the graph is a ___________.

positive, minimum

If the graph of a quadratic function opens upward, then its leading coefficient is _________ and the vertex of the graph is a ___________.

Leading Coefficient Test

The ______________ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

Intermediate Value

The _________________ Theorem states that if "f" is a polynomial function such that f(a) does not equal f(b) , then in the interval (a , b), "f" takes on every value between f(a) and f(b).

Remainder Theorem

The _________________ states that if a polynomial f(x) is divided by x - k , then the remainder is r = f(k).

Fundamental Theorem, Algebra

The ___________________ of ___________ states that is f(x) is a polynomial funtion of degree "n" ( n > 0 ) , then "f" has at least one zero in the complex number system.

axis

The graph of a quadratic function is quadratic about its ________.

vertical

The graph of f(x) = 1/x has a _____________ asymptote at x = 0.

continuous

The graphs of all polynomial functions are __________, which means that the graphs have no breaks, holes, or gaps.

root -1, -1

The imaginary unit "i" is defined as "i"= ____, where "i"^2 = _____.

improper, proper

The rational expression p(x) / q(x) is called __________ if the degree of the numerator is greater than or equal to that of the denominator, and is called __________ if the degree of the numerator is less than that of the denominator.

complex, a + bi

The set of real multiples of the imaginary unit "i" combined with the set of real numbers is called the set of ___________ numbers, which are written in the standard form __________.

Rational Zero

The test that gives a list of the possible rational zeros of a polynomial function is known as the ______________ Test.

Descartes's Rule, signs

The theorem that can be used to determine the possible numbers of positive real zeros and negative real zeros of a function is called ___________ of _________.