Pre Calc Ch 2 Test 1 Vocab

When a real zero x = a of a polynomial function f is of even multiplicity, the graph of f ________ the x-axis at x = a, and when it is of odd multiplicity, the graph of f ________ the x-axis at x = a.

Bounces/touches, crosses

An ________ number has the form a + bi, where a ≠ 0, b ≠ 0.

Complex

The numbers a + bi and a − bi are called ________ ________, and their product is a real number a2 + b2.

Complex Conjugates

The graph of a polynomial function is ________, which means that the graph has no breaks, holes, or gaps.

Continuous and curvy

x3

Cubic

The ________ Theorem states that a polynomial f (x) has a factor (x − k) if and only if f (k) = 0.

Factor Theorem

In the Division Algorithm, the rational expression f (x)d(x) is ________ because the degree of f (x) is greater than or equal to the degree of d(x).

Improper Fraction

The ________ ________ Theorem states that if f is a polynomial function such that f (a) ≠ f (b), then, in the interval [a, b], f takes on every value between f (a) and f (b).

Intermediate Value

A ________ number has the form a + bi, where a ≠ 0, b = 0.

Real

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

Remainder Theorem

A factor (x − a)k, k > 1, yields a ________ ________ x = a of ________ k. 7.

Repeated root, multiplicity

A polynomial function is written in ________ form when its terms are written in descending order of exponents from left to right.

Standard

A shortcut for long division of polynomials is ________ ________, in which the divisor must be of the form x − k.

Synthetic Division

Two forms of the Division Algorithm are shown below. Identify and label each term or function. f(x) = d(x)q(x) + r(x) f(x) = q(x) + r(x) d(x) d(x)

a) division algorithm b) alternate form

When x = a is a zero of a polynomial function f, the three statements below 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 of f.

a) zero/root b) x-a c) x int

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

quadratic, parabola

The imaginary unit i is defined as i = ________, where i2 = ________.

{-1}, -1

x4

Quartic

x5

Quintic

x2

Quadratic

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

Leading coefficient test

x1

Linear

A polynomial function of degree n has at most ________ real zeros and at most ________ turning points.

N, (n-1)

When the graph of a quadratic function opens downward, its leading coefficient is ________ and the vertex of the graph is a ________.

Negative, Max

Linear, constant, and squaring functions are examples of ________ functions.

Polynomial

A polynomial function of x with degree n has the form f(x) = anxn + an−1xn−1 + . . . + a1x + a0 (an ≠ 0), where n is a ________ ________ and an, an−1, . . . , a1, a0 are ________ numbers.

Positive integer, Real

When a is a positive real number, the ________ ________ root of −a is defined as √ −a = √ ai.

Principal square

In the Division Algorithm, the rational expression r(x)/d(x) is ________ because the degree of r(x) less than the degree of d(x).

Proper fraction

A ________ ________ number has the form a + bi, where a = 0, b ≠ 0.

Pure Imaginary