Chapter 2 PreCalc Vocabulary

Lower;upper

A real number b is a(n) ___________ bound for the real zeros of f if no real zeros are less than b, and is a(n) ___________ bound if no real zeros are greater than b

Synthetic division

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

Slant asymptote

For the rational function given by 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 f has a _________ (or oblique) _________________

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 numbers;a+bi

If a is a positive number, the ___________ ________________ root of the negative number -a is defined as the square root as -a = the square root of ai

Touches;crosses

If a real zero of a polynomial function is oven multiplicity, then the graph of f ___________ the x-axis at x=a, and if it is of odd multiplicity then the graph of f ___________ the x-axis at x=a

Conjugate

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

Vertical asymptote

If f(x) -> + or - infinity as x -> a from the left or the right, then x=a is ____________ __________________ of the graph of f

Horizontal asymptote

If f(x) -> b as x -> + or - infinity, then y=b is _________ __________________ 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 ___________

Solution;(x-a);x-intercept

If x=a is a zero of a polynomial function f, then the following three statements are true... (A) x=a is a _____________ of the polynomial equation f(x)=0 (B) _________ is a factor of the polynomial f(x) (C) (a,0) is an __________________ of the graph f

i

Imaginary number; a+bi, a does not equal 0, b does not equal 0

iii

Real number; a+bi, b=0

Linear factorization theorem

The __________ ____________________ _____________ states that if f(x) is a polynomial of degree n(n>0), then f has precisely n linear factors f(x)=An(x-c1)(x-c2)...(x-cn) where c1, c2,...,cn are complex numbers

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) is not equal to f(b), then in the interval [a,b], f takes on every value between f(a) and f(b)

Fundamental theorem of algebra

The _____________________ ______________ of ____________ states that if f(x) is a polynomial of degree n(n>0), then f has at least one zero in the complex number system

Remainder

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

Factor

The __________theorem states that a polynomial f(x) has a factor (x-k) if and only if f(k)=0

Zeros;undefined values

The critical numbers of a rational expression are its ______ and its _______________ ___________

Axis

The graph of a quadratic function is symmetric about its _____

Continuous

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

Square root of -1;-1

The imaginary unit i is defined as i = _______, where i squared = _____

Principal square

The numbers a+bi and a-bi are called ____________ _________, and their product is a real number a squared + b squared

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

Rational zero

The test that gives a list of the possible rational zeros of a polynomial function is called the ______________ _____ test

Descartes' rule of 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 _________

Critical;test intervals

To solve a polynomial inequality, find the _________ numbers of the polynomial, and use these numbers to create ______ _____________ for the inequalities

Quadratic;parabola

A _______________ function is a second-degree polynomial function, and its graph is called a ____________

Standard

A polynomial function is written in ______________ form if its terms are written in descending order of exponents from left to right

Nonnegative integer;real

A polynomial function of degree n and leading coefficient An is a function of the form f(x)=AnXn + An-1XN-1 + ... + A1X + A0 (An does not equal 0) where n is a ____________________ _________and A1 are _____ numbers

N;n-1

A polynomial function of degree n has at most ___ real zeros and at most ___________ turning points

Irreducible over the reals

A quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be ________________ over the _______

ii

Pure imaginary number; a+bi,a=0, b does not equal 0