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piecewise-defined function

piecewise-linear function

step function

greatest integer function

a functions using two or more expressions

a single expression

line segments

f(x)=[[x]]----- the greatest integer less than or equal to x.

piecewise-defined function

a functions using two or more expressions

piecewise-linear function

a single expression

Normal Distribution

Normal Curve

Standard Normal Distribution

Z-score

A type of probability distribution in which the graph is a be…

The graph of a normal distribution that is bell-shaped and is…

The normal distribution with mean 0 and standard deviation 1

The z-value for a particular x-value which is the number of s…

Normal Distribution

A type of probability distribution in which the graph is a be…

Normal Curve

The graph of a normal distribution that is bell-shaped and is…

Equivalent Equations

Addition Property of Equality

Subtraction Property of Equality

Isolate

Equations that have the same solution.

For any real numbers a, b and c.... If a = b, the a + c = b + c

For any real numbers a, b and c.... If a = b, the a - c = b - c

Using properties of equality and inverse operations to get a…

Equivalent Equations

Equations that have the same solution.

Addition Property of Equality

For any real numbers a, b and c.... If a = b, the a + c = b + c

Quadratic function

Quadratic term

Linear term

Constant term

An equation in the form of: ax²+bx+c=0

The "ax²" or first term of a quadratic equation.

The "bx" or second term of a quadratic equation.

The "c" or third term of a quadratic equation.

Quadratic function

An equation in the form of: ax²+bx+c=0

Quadratic term

The "ax²" or first term of a quadratic equation.

permutations

combinations

graphing trig functions: a

graphing trig functions: (b0-c)

specific oder: chronological, favorites, results, placings, e…

no specific order: picking randomly out of a group

amplitude

determines start point, end point, and period

permutations

specific oder: chronological, favorites, results, placings, e…

combinations

no specific order: picking randomly out of a group

variable

algebraic expression

order of operations

monomial

symbols, usually letters, used to represent unknown quantities

contains at least one variable

Used to solve algebraic expressions by replacing each variabl…

an algebraic expression that is a number, a variable, or the…

variable

symbols, usually letters, used to represent unknown quantities

algebraic expression

contains at least one variable

Asymptote

Axis of Symmetry

Complex Fraction

Composition

The line that approaches the curve

A line that splits a graph into symmetrical parts

A fraction with a fraction in the numerator, denominator or b…

f g(x) = f[g(x)] and g f(x) = g[f(x)]

Asymptote

The line that approaches the curve

Axis of Symmetry

A line that splits a graph into symmetrical parts

relation

function

domain

range

any set of points (x,y)

a type of relation in which each element of the domain is pai…

-x's... -independent variable... -input

-y's ... -dependent variable... -output

relation

any set of points (x,y)

function

a type of relation in which each element of the domain is pai…

polynomial

standard form of a polynomial

degree

degree of a polynomial

a monomial or the sum of monials

when the polynomial terms are written in descending order by…

the exponent of the variable in a term

the greatest degree of any term of the polynomial

polynomial

a monomial or the sum of monials

standard form of a polynomial

when the polynomial terms are written in descending order by…

how are matrices named

how to add/subtract matrices

how to multiply a matrix by a scaler

how to multiply a matrix by another ma…

row x column

- matrices must have the same dimensions ... - add/subtract corr…

multiply every entry in the matrix by the scaler

- inner dimensions MUST be the same... - product matrix is the o…

how are matrices named

row x column

how to add/subtract matrices

- matrices must have the same dimensions ... - add/subtract corr…

Systems of Equations

Classifying Polynomials

Binomial Expansion

Specific Term of an Expansion

i. Substitution: if one variable has a coefficent of one... ii.…

Degrees:... 0 - constant... 1 - linear ... 2 - quadratic... 3 - cubic... 4 -…

*Pascal's Triangle... Number of terms = Degree number + one... Firs…

[degree of binomial nCr term # -1] x (first term)^(degree - t…

Systems of Equations

i. Substitution: if one variable has a coefficent of one... ii.…

Classifying Polynomials

Degrees:... 0 - constant... 1 - linear ... 2 - quadratic... 3 - cubic... 4 -…

quadratic term

linear term

constant term

vertex

In algebra, a quadratic function, a quadratic polynomial, a p…

A linear equation is an algebraic equation in which each term…

Constant Term. The term in a simplified algebraic expression…

Vertex typically means a corner or a point where lines meet.…

quadratic term

In algebra, a quadratic function, a quadratic polynomial, a p…

linear term

A linear equation is an algebraic equation in which each term…

Constraints

Consistent Dependent System

Objective Function

Feasible Region

Boundaries used in linear programming

A system of equations with an infinite number of solutions

The function being maximized or minimized in linear programming

The area of intersection of a system of inequalities

Constraints

Boundaries used in linear programming

Consistent Dependent System

A system of equations with an infinite number of solutions

Formula for if something varies directly

How do you solve: y varies directly wi…

Formula for varying jointly

Formula for y varies inversely as x

y=kx

You would plug y and x into y=kx and solve for k then use tha…

y=kxz

y=k/x

Formula for if something varies directly

y=kx

How do you solve: y varies directly wi…

You would plug y and x into y=kx and solve for k then use tha…

natural numbers

whole numbers

integers

rational numbers

used to count... 1,2,3

natural numbers and zero... 0,1,2,3

are the natural numbers, their opposites, and zero... -3,-2,-1,0…

can be written as fractions, terminating decimals, and repeat…

natural numbers

used to count... 1,2,3

whole numbers

natural numbers and zero... 0,1,2,3

Exponent

Degree of a polynomial

Relative minimum

Greatest Common Factor --GCF

A mathematical notation that implies the number of times a nu…

The degree is the term with the greatest exponent in a polyno…

A value of the function at a down to up turning point.

The highest number that divides exactly into two or more numb…

Exponent

A mathematical notation that implies the number of times a nu…

Degree of a polynomial

The degree is the term with the greatest exponent in a polyno…

linear programming

linear system

constraint

consistent system

a method of finding a maximum and minimum value of a linear f…

a system of equations containing only linear equations

one of the inequalities that define the feasible region in a…

system of equations with at least one solution

linear programming

a method of finding a maximum and minimum value of a linear f…

linear system

a system of equations containing only linear equations

Translation formula horizontal

Translation formula vertical

Compression/stretch (horizontal)

Compression/stretch (vertical)

f(x) -> f(x - h)... F of x minus h

f(x) -> f(x) + K ... F of x plus K... remember: vertiKal

f(x) -> f(1/bx)... F of 1 divided by B times X

f(x) -> a * f(x)... A times F of x

Translation formula horizontal

f(x) -> f(x - h)... F of x minus h

Translation formula vertical

f(x) -> f(x) + K ... F of x plus K... remember: vertiKal

Exponential function

Exponential growth

Exponential decay

Asymptote

A function with the general form y=ab^x where a does not equa…

As the value of X increases, the value of y increases... Is mode…

As the value of X increases the value of y decreases

A line that a graph approaches but never touches

Exponential function

A function with the general form y=ab^x where a does not equa…

Exponential growth

As the value of X increases, the value of y increases... Is mode…

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the nega…

If both terms are opposite signs they can be crossed out and…

Raising a negative number to a power

When raising a negative number to a power always put the nega…

Factoring ax²+bx+c

Exponential Function =

exponential growth=

exponential decay=

Asymptote=

y=ab^x ... *b --> base, positive # other than 1... *x --> exponent…

as x increases, y increases

as x increases, y decreases

(always a dotted line)... a line your graph approaches, but neve…

Exponential Function =

y=ab^x ... *b --> base, positive # other than 1... *x --> exponent…

exponential growth=

as x increases, y increases

absolute value of a number

order of operations

algebraic expression

terms

its distance from zero indicated by parallel bars on each sid…

1. parentheses... 2. powers... 3. multiplication or division from l…

an arrangement of variables and figures along with mathematic…

the parts of an expression separated by a + or a - sign

absolute value of a number

its distance from zero indicated by parallel bars on each sid…

order of operations

1. parentheses... 2. powers... 3. multiplication or division from l…

Axis of Symmetry

Domain

Function

Function Notation

The line that divides a figure into two parts that are mirror…

The set of all inputs, or x-coordinates, of the ordered pairs

A relation in which each element of the domain corresponds wi…

Shows the function name f, and also represents the range valu…

Axis of Symmetry

The line that divides a figure into two parts that are mirror…

Domain

The set of all inputs, or x-coordinates, of the ordered pairs

Binomial

Constant

Quotient

Degree of a monomial

The sum or difference of two unlike monomials

A monomial without a variable - its degree always equal to zero

The answer to a division problem

The sum of the powers of the variables of the monomial

Binomial

The sum or difference of two unlike monomials

Constant

A monomial without a variable - its degree always equal to zero

g r a p h

zero slope

linear equation

piecewise function

represents numerical information spatially

the slope of a horizontal line

an equation in two variables whose graph is a line

a function composed of 2 or more functions

g r a p h

represents numerical information spatially

zero slope

the slope of a horizontal line

open sentence

equation

solution

Addition Property of Equality

A mathematical statement that can be either true or false dep…

A mathematical sentence stating that two mathematical express…

The number that makes the open sentence or equation true.

If a = b; then a + c = b + c.

open sentence

A mathematical statement that can be either true or false dep…

equation

A mathematical sentence stating that two mathematical express…

Opposite

Reciprocal

Term

Coefficient

The opposite or additive inverse of any number. ... ( a is -a )

The reciprocal or the multiplicative inverse of any nonzero n…

An expression that is a number, a variable, or the product of…

The numerical factor of a term.

Opposite

The opposite or additive inverse of any number. ... ( a is -a )

Reciprocal

The reciprocal or the multiplicative inverse of any nonzero n…

Consistent Independent

Consistent Dependent

Inconsistent

Feasible Region

A system of equations with one solution

A system of equations with an infinite number of solutions.

A system of equations that has no solutions

The area of intersection of a system of inequalities

Consistent Independent

A system of equations with one solution

Consistent Dependent

A system of equations with an infinite number of solutions.