Unit 2 Section 2.5 - 2.9 Vocabulary

The theorem that can be used to determine the possible numbers of positive real zeros and negative real zeros of a function is called _____. (Sec. 2.3)

Descartes's Rule of Signs Theorem

The _____ states that if f(x) is a polynomial function of degree n (n>0), then f has at least one zero in the complex number system. (Sec. 2.5)

Fundamental Theorem of Algebra

The _____ is used to determine the left-hand and right-hand end behavior of the polynomial functions. (Sec. 2.2)

Leading Coefficient Test

The _____ states that if f(x) is a polynomial of degree n, then f has precisely n linear factors f(x) = a,n(x-c1)(x-c2)...(x-cn) where c1, ... cn are complex numbers. (Sec. 2.5)

Linear Factor Theorem

The test that gives a list of all POSSIBLE rational zeros of a polynomial is known as _____. (Sec. 2.3)

Rational Zeros Test

The _____ states that is a polynomial f(x) is divided by x - k, then the remainder r = f(k). (Sec. 2.3)

Remainder Theorem

If a + bi is a complex zero of a polynomial with real coefficients, then so is its _________, a - bi. (Sec. 2.5)

complex conjugate

The set of real multiples of the imaginary unit I combined with the set of real numbers is called the set of _____, written in standard form look like _____.

complex numbers, a + bi

The graphs of all polynomial functions are ____, which means that the graphs have no breaks, holes, or gaps. (Sec. 2.2)

continuous

When graphing by hand, what characteristics should you look for and identify? (Sec. 2.7)

domain, vertical asymptote, horizontal asymptote, slant asymptote, holes

To write a "model" is the same to write an _____. (Sec. 2.8)

equation

If f(x) --> b as x --> +-infinity, then y = b is a _____ of the graph of f. (Sec. 2.6)

horizontal asymptote

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 the denominator. (Sec. 2.3)

improper, proper

A quadratic factor that cannot be factored future as a product of linear factors containing real numbers is said to be a _____ over the _____. (Sec. 2.5)

irreducible prime numbers, reals

The graph of a quadratic function is symmetric about its _____. (Sec. 2.1)

line of symmetry

A scatter plot with either a positive or a negative correlation can be modeled by a _____ equation. (Sec. 2.8)

linear

A polynomial function of the degree n has the most _____ real zeros and at most _____ turning points. They are called relative extrema. (Sec. 2.2)

n, n-1

If the graph of a quadratic function opens downward, then its leading coefficient is _____ and the vertex of the graph is a _____. (Sec. 2.1)

negative, maximum

A polynomial function of degree n and leading coefficient An is a function of the form f(x) = anx^n.... where n is _____ and An, An-1, ..., a , A0 are _____. (Sec. 2.1)

non-negative integer, real

If the graph of a quadratic function opens upward, then its leading coefficient is _____ and the vertex of the graph is a _____. Sec. (2.1)

positive, minimum

What kind of complex numbers are the following. a) a + bi, a = 0, b =/ 0 b) a + bi, b = 0 c) a + bi, a =/0, b =/0

pure imaginary, real number, imaginary number

A scatter plot that appears parabolic can be modeled by a _____ equation. (Sec. 2.8)

quadratic

A _____ function is a second-degree polynomial function, and its graph is called a _____. (Sec. 2.1)

quadratic, parabola

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 _________ _________. (Sec. 2.6)

ration functions

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

real, imaginary

f(x) = d(x)q(x) + r(x) f(x)/d(x) = q(x) + r(x)/d(x) r(x) = _____ q(x) = _____ f(x) = _____ d(x) = _____ (Sec. 2.3)

remainder, quotient, dividend, divisor

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

root -1, -1

For the rational function f(x) = N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), then the graph of f has a _____. ( Sec. 2.7)

slant asymptote

If x = a is a zero of a polynomial function f, then the following are true. a) x = a is a _____ of the polynomial function f(x) = 0 b) _____ is a factor of the polynomial f(x). c) (a,0) is a(n) _____ of the graph of f. (Sec. 2.2)

solution, (x-a), x-intercept

An alternative method to the long division of polynomials is called _____, in which the divisor must be of the form x - k. (Sec. 2.3)

synthetic division

If a zero of a polynomial function 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 (Sec. 2.2)

touches, crosses

A real number b is an _____ for the real zeros of f if no zeros are greater than b and is _____if no real zeros are less than b. (Sec. 2.3)

upper bound, lower bound

The standard form of a quadratic is the same as the _____. (Sec 2.1)

vertex form

The graph of f(x) = 1/x has a _____ asymptote of x = 0. (Sec. 2.7)

vertical

If f(x) --> +-infinity as x -->a from the left (or right), then x = a is a _____ of the graph of f. (Sec 2.6)

vertical asymptote