#### Study sets matching "advanced algebra"

#### Study sets matching "advanced algebra"

Natural numbers

Whole numbers

Integers

Rational numbers

The numbers used for counting: 1, 2, 3, 4

Natural numbers and zero (0, 1, 2, 3, 4)

Natural numbers (positive integers), zero, and negative integ…

All the numbers can be written as quotients as integers. Must…

Natural numbers

The numbers used for counting: 1, 2, 3, 4

Whole numbers

Natural numbers and zero (0, 1, 2, 3, 4)

Dependent Variable

Independent Variable

Function

Domain

a variable that provides the output values of a function

a variable that provides the input values of a function

a relation that assigns exactly one value in the range to eac…

the possible values for the input of a funtion

Dependent Variable

a variable that provides the output values of a function

Independent Variable

a variable that provides the input values of a function

Variable

Expression

Algebraic Sentence

Equation

a letter that can replaced by a number(x)

connects variables and numbers( x,/,-,+)(x+2)

connect two expressions (<,>,less or greater than,=) (x+2=7)

A sentence that has an equal sign

Variable

a letter that can replaced by a number(x)

Expression

connects variables and numbers( x,/,-,+)(x+2)

coefficient matrix

Cramer's Rule

determinant

dilation

matrix used with the coefficients of a system

method of solving systems using determinants

a number associated with a square matrix

a transformation that enlarges or reduces a figure

coefficient matrix

matrix used with the coefficients of a system

Cramer's Rule

method of solving systems using determinants

Direct, inverse, and mixed

Arithmetic, harmonic, geometric

D= a2 minus a1

X = a+b over 2

Three kinds of variation

Three types of progressions

In arithmetic progression, how do you find the d? Hahaha

How do you find the arithmetic mean?

Direct, inverse, and mixed

Three kinds of variation

Arithmetic, harmonic, geometric

Three types of progressions

Expected value

Variance

Outlier

Population

The weighted average of the possible outcomes

Average of the squared differences from the mean

An extreme value that is much less than or much greater than…

The entire group of people or objects that you want imformati…

Expected value

The weighted average of the possible outcomes

Variance

Average of the squared differences from the mean

Histogram

Interquartile Range

Qualitative Data

Quantitative Data

a graph that displays data form a frequency table

the difference between the first and third quartile

data that name qualities

data that measures quantity and can be described numerically

Histogram

a graph that displays data form a frequency table

Interquartile Range

the difference between the first and third quartile

Factor

Factor of a polynomial (P(x))

Perfect square

Perfect cube

a number or quantity that when multiplied with another produc…

any polynomial which divides evenly into P(x)

the product of a rational number multiplied by itself

the product of a rational number multiplied by itself three t…

Factor

a number or quantity that when multiplied with another produc…

Factor of a polynomial (P(x))

any polynomial which divides evenly into P(x)

Completing the Square

Complex Conjugate

Complex Number

Expression

The process of adding a term to a quadratic expression of the…

Two complex numbers of the form a+bi and a-bi.

A number a+bi where a and b are real numbers and i is the ima…

A symbol or a combination of symbols representing a value, re…

Completing the Square

The process of adding a term to a quadratic expression of the…

Complex Conjugate

Two complex numbers of the form a+bi and a-bi.

Monomials

Binomials

Trinomials

Polynomial

A real number, a variable, or a product of a real number and…

A polynomial of two terms

A polynomial of three terms

A monomial or the sum or difference of two or more monomials

Monomials

A real number, a variable, or a product of a real number and…

Binomials

A polynomial of two terms

radicand

inverse relation

identity

rationalizing the denominator

the expression under the radical sign

reverse the coordinates of the ordered pairs of a relation

every element of the domain maps to the same value of the range

one of the steps that may be needed to simplify a radical

radicand

the expression under the radical sign

inverse relation

reverse the coordinates of the ordered pairs of a relation

Addition of perfect cube

Difference of perfect cube

Looking for holes

Finding vertical asymptotes

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

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

After you have factored and simplified the rational function,…

Set the denominator equal to zero and solve for x

Addition of perfect cube

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

Difference of perfect cube

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

Range

Domain

No solution

All real numbers

Distance between highest and lowest scores in a set of data,…

The set of input values of a function.

a number and a number equal each other but they actually don'…

Numbers are the same on each side of the equal sign

Range

Distance between highest and lowest scores in a set of data,…

Domain

The set of input values of a function.

Absolute Value

Like Terms

Coefficient

Open Sentence

The distance a number is from zero.

Terms with exactly the same variable(s) to the same power(s).

The number in front of the variable.

An equation that contains one of more variable(s).

Absolute Value

The distance a number is from zero.

Like Terms

Terms with exactly the same variable(s) to the same power(s).

absolute value

relation

domain

range

how many units from zero on a number line

pairing of input values with output values

all possible input values (x values)

all possible output values (y values)

absolute value

how many units from zero on a number line

relation

pairing of input values with output values

Polynomial

Constant

Monomial

Binomial

The sum or difference of two or more monomials.

A term with degree 0: ie. a number alone, with no variable.

An algebraic expression that is a constant, a variable, or a…

The sum or difference of two monomials

Polynomial

The sum or difference of two or more monomials.

Constant

A term with degree 0: ie. a number alone, with no variable.

**Exponential and Logarithmic Functions**

Which of the following describes the t…

What are the domain and range of f(x)…

Which statement best describes the dom…

**Graphing Exponential Functions**

shift 4 units left, reflect over the x-axis, shift 2 units do…

The domain is all real numbers. The range is all real numbers…

p(x) and q(x) have the same domain and the same range.

**Exponential and Logarithmic Functions**

**Graphing Exponential Functions**

Which of the following describes the t…

shift 4 units left, reflect over the x-axis, shift 2 units do…

Absolute Value

Coefficient

Composition of Functions

Function

How far a number is from zero. The magnitude of a real number…

A number used to multiply a variable. Placed before the varia…

Applying one function to the the results of another. Ex: g(f(…

A special relationship where each input has one output.

Absolute Value

How far a number is from zero. The magnitude of a real number…

Coefficient

A number used to multiply a variable. Placed before the varia…

Zero of a polynomial

Root of a polynomial

Complex roots

Complex Conjugate

a number that, when plugged in for the variable, makes the fu…

a number that, when plugged in for the variable, makes the fu…

a root of a polynomial function that contains a complex number

each of two complex numbers having their real parts identical…

Zero of a polynomial

a number that, when plugged in for the variable, makes the fu…

Root of a polynomial

a number that, when plugged in for the variable, makes the fu…

Domain

Range

Extraneous Solution

Radical expression

the set of values of the independent variable(s) for which a…

the set of y-values (or output values) of a function or relat…

a solution of the simplified form of the equation that does n…

any expression containing a radical

Domain

the set of values of the independent variable(s) for which a…

Range

the set of y-values (or output values) of a function or relat…

Real numbers

Rational numbers

Irrational numbers

(u+v)3

All rational and irrational numbers. Can be represented on th…

Real numbers that can be written as the ratio of two integers.

Real numbers that cannot be written as the ratio of two integ…

U³+3U²V+3UV²+V³

Real numbers

All rational and irrational numbers. Can be represented on th…

Rational numbers

Real numbers that can be written as the ratio of two integers.

Polynomial

0 Degree

1st Degree

2nd Degree

A monomial, or sum of monomial(s)... Ex: 2x^(3) - 5x^(2) - 2x +…

constant... x ... 1 term... monomials

linear... x^(1) + 2... 2 terms ... binomial

quadratic... x^(2)... 1 term ... monomial

Polynomial

A monomial, or sum of monomial(s)... Ex: 2x^(3) - 5x^(2) - 2x +…

0 Degree

constant... x ... 1 term... monomials

Angles

Initial Side

Terminal Side

θ (Theta)

Two rays connected by a common endpoint (vertex)

Positive x-axis. Does not move.

Moves to show angle position and size.

Letter than names an angle.

Angles

Two rays connected by a common endpoint (vertex)

Initial Side

Positive x-axis. Does not move.

Exponential expression

Exponential equations

Logarithmic expression

Logarithmic equation

a mathematical expression consisting of a constant raised to…

an equation involving exponential functions of a variable

the power to which a base, such as 10, must be raised to prod…

an equation involving logarithmic functions of a variable

Exponential expression

a mathematical expression consisting of a constant raised to…

Exponential equations

an equation involving exponential functions of a variable

Radian

Degree

Unit circle

Coterminal angles

a unit of angle, equal to an angle at the center of a circle…

a unit of measurement of angles, one three-hundred-and-sixtie…

the circle of radius one centered at the origin (0, 0) in the…

angles which, drawn in standard position, share a terminal side

Radian

a unit of angle, equal to an angle at the center of a circle…

Degree

a unit of measurement of angles, one three-hundred-and-sixtie…

Coefficient

Degree

Binomial

Trinomial

a number multiplied by a variable

the greatest exponent of its variable

an algebraic expression of the sum or the difference of two t…

an algebraic expression of the sum or the difference of three…

Coefficient

a number multiplied by a variable

Degree

the greatest exponent of its variable

Pythagorean Theorem

Angle of Elevation

Angle of Depression

Sine

In any right angle, the sum of the squares of the lengths of…

An angle from the horizontal UP to the line of site.

An angle from the horizontal DOWN to the line of site.

For any given angle in a right triangle, a trigonometric func…

Pythagorean Theorem

In any right angle, the sum of the squares of the lengths of…

Angle of Elevation

An angle from the horizontal UP to the line of site.

Radical Function

Square Root Function

Inverse Functions

Index

A function that contains the root of a variable.

A function that contains a square root of a variable.

Two functions are inverse functions if and only if both of th…

The value of n by the radical sign indicates to what root the…

Radical Function

A function that contains the root of a variable.

Square Root Function

A function that contains a square root of a variable.

Fraction meanings

Equations

Algebraic tests

Motion

numerator-range... denominator- domain

undefined means x doesn't change

solve be making equation f(-x)... f(x)-even or the same... -f(x)- o…

rest and change direction set equal to zero

Fraction meanings

numerator-range... denominator- domain

Equations

undefined means x doesn't change

Absolute value

Composite function

Domain

Equation

The distance from zero; when simplifying inside of it, the va…

A combination of two functions such that the output from the…

The possible input values (typically the x-values)

A statement that two algebraic expressions are equal

Absolute value

The distance from zero; when simplifying inside of it, the va…

Composite function

A combination of two functions such that the output from the…

Transformation

Pre-Image

Image

Reflection

A general term to manipulate a shape of a point, a line, or a…

Original Image

New Image after a transformation

Type of rigid transformation in which the pre-image is flippe…

Transformation

A general term to manipulate a shape of a point, a line, or a…

Pre-Image

Original Image