Ch.5 - 8 Vocabulary

Question 1

Polynomial in one variable

Answer 1

An expression of the form an x^n + an-1 x^n-1 + … + a2 x^2 + a1 x + a0, where an is not 0, all the coefficients are real numbers, and n is a nonnegative integer.

Question 2

Leading coefficient

Answer 2

The coefficient of the first term of a polynomial in standard form.

Question 3

Polynomial function

Answer 3

A continuous function that can be described by a polynomial in one variable.

Question 4

Power function

Answer 4

The simplest form of a polynomia function in the form of f(x)= ax^b, where a and b are nonzero real numbers.

Question 5

Quartic function

Answer 5

A polynomial function with the degree of four.

Question 6

Quintic function

Answer 6

A polynomial function with the degree of five.

Question 7

End behavior

Answer 7

The behavior of the graph of f(x) as x approaches positive or negative infinity, determined by the degree and leading coefficient of the function.

Question 8

Location principle

Answer 8

If the value of f(x) changes signs from one value of x to the next, then there is a zero between those two values.

Question 9

Relative maximum

Answer 9

A point with no other nearby points that have a greater y-coordinante.

Question 10

Relative minimum

Answer 10

A point with no other nearby points that have a lesser y-coordinate.

Question 11

Extrema

Answer 11

The maximum and minimum values of a function.

Question 12

Turning point

Answer 12

A point that is a relative maximum or minimum of the graph in which the graph changes direction.

Question 13

Prime polynomial

Answer 13

A polynomial that cannot be factored.

Question 14

Quadratic form

Answer 14

au^2+bu+c, which a polynomial in x could be rewritten as.

Question 15

Sum of two cubes (formula)

Answer 15

a^3 + b^3 = (a+b)(a^2-ab+b^2)

Question 16

Difference of two tubes (formula)

Answer 16

a^2-b^3 = (a-b) (a^2+ab+b^2)

Question 17

Synthetic substitution

Answer 17

Applying the Remainder Theorem using synthetic division to evaluate a function.

Question 18

Depressed polynomial

Answer 18

The quotient after dividing a polynomial by a binomial, which would have a degree one less than the original polynomial.

Question 19

Remainder theorem

Answer 19

If a polynomial is divided by x-r, the remainder isa constant P(r).

Question 20

Factor theorem

Answer 20

If the binomial x-r is a factor of the polynomial P(x) if and only if P(r)=0.

Question 21

The fundamental theorem of algebra

Answer 21

Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.

Question 22

Corollary to the fundamental theorem of algebra

Answer 22

A polynomial equation of degree n has exactly n roots in the set of complex numbers, including repeated roots.

Question 23

Descartes’ rule of signs

Answer 23

The number of positive real zeros of P(x) is the same as the number of changes in sign of the coefficient of the terms, or is less than this by an even number.
The number of negative real zeros of P(x) is that in terms of P(-x).

Question 24

Complex conjugates theorem

Answer 24

Let a and b be real numbers and b is not 0. If a+bi is a zero of a polynomial function with real coefficients, then a-bi is also a zero of the function.

Question 25

Rational zero theorem

Answer 25

If P(x) is a polynomial function with integral coefficients, then every rational zero of P(x) = 0 is of the form p/q, a rational number in simplest form, where p is a factor of the constant term and q is a factor of the leading coefficient.

Question 26

Composition of functions

Answer 26

The results of one function are used to evaluate a second function.

Question 27

Inverse relation

Answer 27

The set of ordered pair obtained by exchanging the coordinates of each ordered pair.

Question 28

Inverse function

Answer 28

The inverse function of f(x) is written as f-1(x), f(a) = b if and only if f-1(b) = a.

Question 29

Square root function

Answer 29

A function that contains the square root of a variable.

Question 30

Radical function

Answer 30

A function in which the variable is under the radical sign.sign.

Question 31

Square root inequality

Answer 31

An inequality involving square roots of a variable.

Question 32

Radicand

Answer 32

The number under the radical sign

Question 33

Index

Answer 33

For nth root (the inverse of raising a number to the nth power), the index is n.

Question 34

Primary root

Answer 34

The nonnegative root when there is more than one real root and the index is even.

Question 35

Rationalizing the denominator

Answer 35

Multiplying the numerator and denominator by a quantity so that the radicand of the denominator has an exact root to eliminate radicals from the denominator.

Question 36

Like radical expressions

Answer 36

Radicals with the same index and radicand.

Question 37

Conjugates

Answer 37

a√b + c √d and a√b - c √d are conjugates if a,b,c,d are all rational numbers.

Question 38

Radical equation

Answer 38

An equation that include radical expressions, can be solved by raising each side of the equation to a power.

Question 39

Extraneous solution

Answer 39

The result of an equation that does not satisfy the original equation.

Question 40

Radical inequality

Answer 40

An inequality that has a variable in the radicand.

Question 41

Exponentail function

Answer 41

A function where the base is a constant and the exponent is the independent variable.

Question 42

Exponential growth

Answer 42

A function of the form f(x)=b^x, where b > 1.

Question 43

Asymptote

Answer 43

A line that the graph of the function approaches.

Question 44

Growth factor

Answer 44

The base of the exponential function, 1+r.

Question 45

Exponential decay

Answer 45

A function of the form f(x) = b^x, where 0<b></b>

Question 46

Decay factor

Answer 46

The base of the exponential function, 1-r.

Question 47

Exponential equation

Answer 47

An equation in which variables occur as exponents.

Question 48

Compound interest

Answer 48

Interest paid on the principal of an investment and any previously earned interest.

Question 49

Exponential inquality

Answer 49

An inequality involving exponential functions.

Question 50

Logarithm

Answer 50

X=b^y, the variable y is the logarithm of x.

Question 51

Logarithmic function

Answer 51

A function in the form y=logbx, where b is not 1.

Question 52

Logarithmic equation

Answer 52

Contains one or more logarithms.

Question 53

Logarithmic inequality

Answer 53

An inequality that involves logarithms.

Question 54

Product property of logarithms

Answer 54

Logx(ab) = logx(a)+logx(b)

Question 55

Quotient property of logarithms

Answer 55

Logx(a/b) = logx(a)-logx(b)

Question 56

Power property of logarithms

Answer 56

Logb(m^p) = p logb(m)

Question 57

Common logarithms

Answer 57

Base 10 logarithms.

Question 58

Change of base formula

Answer 58

Loga(n) = logb(n) / logb(a)

Question 59

Natural base

Answer 59

An irrational number with the value of 2.71828

Question 60

Natural base exponential function

Answer 60

An exponential function with base e.

Question 61

Natural logarithm

Answer 61

The inverse of a natural base exponential function, often abbreviated as ln.

Question 62

Rate of continuous growth

Answer 62

Represented as k in an exponential growth function,

f(t) = ae^kt

Question 63

Rate of continuous decay

Answer 63

Represented as k in an exponential decay function,

f(t) = ae^-kt

Question 64

Logistic growth model

Answer 64

Represents growth that has a limiting factor,

f(t) = c / (1+ae^-bt) with a,b,c all being positive constant and b

Question 65

Rational expression

Answer 65

A ratio of two polynomial expressions.

Question 66

Complex fraction

Answer 66

A rational expression with a numerator and/or denominator that is also a rational expression.

Question 67

Reciprocal function

Answer 67

A function with an equation of the form f(x) = 1/a(x), where a(x) is a linear function and does not equal to 0.

Question 68

Hyperbola

Answer 68

The shape of the graph of a reciprocal function.

Question 69

Rational function

Answer 69

A function with an equation of the form f(x) = a(x)/b(x)m where a(x) and b(x) are both polynomial functions and b(x) does not equal to 0.

Question 70

Vertical asymptote

Answer 70

b(x) = 0.

Question 71

Horizontal asymptote

Answer 71

If the degree of a(x) is greater, no horizontal asymptote.
If the degree of a(x) is less, f(x) = 0.
If the degrees are equal, f(x) = leading coefficient of a(x) / leading coefficient of b(x).

Question 72

Oblique asymptote

Answer 72

if the degree of a(x) minus that of b(x) is 1, f(x) = a(x) / b(x) with no remainder is the oblique asymptote.

Question 73

Direct variation

Answer 73

Can be expressed in the form y=kx.

Question 74

Constant of variation

Answer 74

The value k in the equation y=kx.

Question 75

Joint variation

Answer 75

When one quantity varies directly as the product of the two or more other quantities, y=kxz.

Question 76

Inverse variation

Answer 76

When the product of two quantities is equal to a constant k, xy=k, y=k/x.

Question 77

Combined variation

Answer 77

When one quantity varies directly and/or inversely as two or more other quantities.

Question 78

Rational equations

Answer 78

Equations that contain one or more rational expressions.

Question 79

Weighted average

Answer 79

The method for finding the mean of a set of numbers in which some elements carry more importance.

Question 80

Rational inequalities

Answer 80

Inequalities that contain one more or rational expressions.