#### Study sets matching "honors algebra iii differental calculous"

#### Study sets matching "honors algebra iii differental calculous"

describe the parent function of a line…

describe the parent function of a abso…

what is the direct variation formula

how do you find x intercept and y inte…

y=x

y= /x/

y=kx or k- y/x

set the other to zero. For example if trying to find x interc…

describe the parent function of a line…

y=x

describe the parent function of a abso…

y= /x/

Algebraic Expression

Coefficient

Compound Inequality

Compound Statement

An expression that contains at least one variable.

A number that is multiplied by a variable.

Two inequalities that are combined into one statement by the…

Two statements that are connected by the word and or or.

Algebraic Expression

An expression that contains at least one variable.

Coefficient

A number that is multiplied by a variable.

X-intercept

Slope-intercept form

Direct variation

Quadrant

The x-coordinate of a point where a graph crosses the x-axis

A linear equation written in the form y=mx+b where m is the s…

The relationship of two variables x and y if there is a nonze…

The four regions into which the coordinate plane is divided b…

X-intercept

The x-coordinate of a point where a graph crosses the x-axis

Slope-intercept form

A linear equation written in the form y=mx+b where m is the s…

Solution

Inconsistant

Consistant

Consistent and Independent

The ordered pair that satisfies each equation in the system

A system with no solution, if the lines are parallel

A system with at least one solution

A system with exactly one solution

Solution

The ordered pair that satisfies each equation in the system

Inconsistant

A system with no solution, if the lines are parallel

parent function

transformation

translation

reflection

The most basic function in a family. Functions in the same fa…

Changes the size, shape, position, or orientation of a graph.

A transformation that shifts a graph horizontally and/or vert…

A transformation that flips a graph over a line called the li…

parent function

The most basic function in a family. Functions in the same fa…

transformation

Changes the size, shape, position, or orientation of a graph.

Solution of a System

Linear System

System of Equations

Inconsistent

A set of values for the variables that makes all the equation…

A set that consists of linear equations.

A set or two or more equations

Solution of a System

A set of values for the variables that makes all the equation…

Linear System

A set that consists of linear equations.

Lesson 1 Objectives

explicit formula

recursive formula

sequence

1. Identify mathematical patterns found in a sequence... 2. Use…

A formula that expresses the nth term of a sequence in terms…

A formula that defines the terms in a sequence by relating ea…

An ordered list of numbers.

Lesson 1 Objectives

1. Identify mathematical patterns found in a sequence... 2. Use…

explicit formula

A formula that expresses the nth term of a sequence in terms…

Equation for arithmetic sequence

what makes an equation linear?

What is standard form?

When solving for the x intercept what…

an = a + (n - 1) d... a = first term in sequence... d = common diff…

No exponents higher than 1 ... No multiplication or division of…

Ax + By = C

y = 0

Equation for arithmetic sequence

an = a + (n - 1) d... a = first term in sequence... d = common diff…

what makes an equation linear?

No exponents higher than 1 ... No multiplication or division of…

Relation

Domain

Rnage

Function

A pair of data w/ no special rules - set of ordered pairs

Set of all inputs, independent values

Set of all outputs, dependent values

A relation for which every value from the set of allowable in…

Relation

A pair of data w/ no special rules - set of ordered pairs

Domain

Set of all inputs, independent values

Family of Functions

Linear Functions

Parameter

Parent Function

A set of functions whose graphs have basic characteristics in…

A function that can be written in the form y=mx+b, where x is…

One of the constants in a function or equation that may be ch…

The most basic function of a family of functions, or the orig…

Family of Functions

A set of functions whose graphs have basic characteristics in…

Linear Functions

A function that can be written in the form y=mx+b, where x is…

Arithmetic Sequence

Common Difference

Constant

Constant of Variation

A numerical pattern that increases or decreases at a constant…

The difference between the terms in an arithmetic sequence.

A monomial that is a real number.

The number K in equations of the form y=Kx

Arithmetic Sequence

A numerical pattern that increases or decreases at a constant…

Common Difference

The difference between the terms in an arithmetic sequence.

terminating decimal

repeating decimal

bar notation

rational number

when the division ends with a remainder of zero

when the division repeats a pattern without end

a bar that is placed over the digit(s) that repeat

any number that can be written as a fraction (ratio)

terminating decimal

when the division ends with a remainder of zero

repeating decimal

when the division repeats a pattern without end

How can you tell if a function is even?

How can you tell if a function is odd?

What is the formula for a translation…

What is the formula for a translation…

A function is even if f(x)=f(-x)

A function is odd if f(x)=-f(-x)

y=f(x-c)

y=f(x+c)

How can you tell if a function is even?

A function is even if f(x)=f(-x)

How can you tell if a function is odd?

A function is odd if f(x)=-f(-x)

What are the zeros of a function

What direction is increasing on a graph

What direction is decreasing on a graph

We say that a function f is increasing…

x intercepts

Northwest

southeast

For any x1 < x2, then f(x1) < f(x2)

What are the zeros of a function

x intercepts

What direction is increasing on a graph

Northwest

Transformation

Translation

Dialation

Reflection

Changes the position or size of a figure.

Moves a figure up, down, left or right.

Makes the graph narrower than the parent graph or wider than…

Flips a figure across a line.

Transformation

Changes the position or size of a figure.

Translation

Moves a figure up, down, left or right.

Function

Function rule

Domain

Range

A relation where each input has exactly one output; no two x-…

An equation that describes a function

The set of input values (x-coordinate) of a function.

The set of output (y-coordinate)values of a function.

Function

A relation where each input has exactly one output; no two x-…

Function rule

An equation that describes a function

how can you tell whether 2 equations a…

how can you tell whether 2 equations a…

what is slope- intercept form?

what is point- slope form?

they have the same slope

their slopes are opp. reciprocal.

how can you tell whether 2 equations a…

they have the same slope

how can you tell whether 2 equations a…

their slopes are opp. reciprocal.

Identity equation

What is that sign for identity solutions

No Solution Equation

What is the sign for a no solution equ…

An equation in which all real number are soluyions

"All Real Numbers"

An equation in which none of the real numbers are a solution.

"No Real Solution"

Identity equation

An equation in which all real number are soluyions

What is that sign for identity solutions

"All Real Numbers"

Equivalent equations

Inverse operation

Solution step

Linear equation in one variable

Equations with the same solutions as the original equation ar…

Operations that undo each other such as addition and subtract…

The result of applying a transformation to an equation when s…

An equation in which the variable is raised to the first powe…

Equivalent equations

Equations with the same solutions as the original equation ar…

Inverse operation

Operations that undo each other such as addition and subtract…

Relation

Function

Input

Output

A set of ordered pairs. Inputs can have different outputs (1…

A relation where every input has ONLY 1 unique output, but di…

X, domain, independent variables

Y, range, dependent variables

Relation

A set of ordered pairs. Inputs can have different outputs (1…

Function

A relation where every input has ONLY 1 unique output, but di…

Binomial Theorem

Complex Conjuate

Complex Numbers

Conjugate Zeros Theorem

For any binomial (a+b) and any positive integer n, ... (a+b)^n =…

Complex numbers with the same digits, but different signs.... Ex…

Includes imaginary numbers, real numbers, irrational numbers,…

If P(x) is a polynomial with real coefficients and if a +bi (…

Binomial Theorem

For any binomial (a+b) and any positive integer n, ... (a+b)^n =…

Complex Conjuate

Complex numbers with the same digits, but different signs.... Ex…

What is a system of equations?

What is a linear system?

What can you do with systems?

How do you test to see if a point work…

A set of two or more equations

A set with lines (system with lines)

1) See if points work as a solution... 2) Solve systems using a…

You substitute the X and Y values into both equations and sol…

What is a system of equations?

A set of two or more equations

What is a linear system?

A set with lines (system with lines)

Open Sentence

Equation

Solution

Inverse Operation

a mathematical sentence containing one or more variables

a mathematical sentence stating that two mathematical express…

a replacement value that makes an open sentence true

operation used to undo another operation

Open Sentence

a mathematical sentence containing one or more variables

Equation

a mathematical sentence stating that two mathematical express…

Continuous Graph

Discrete Graph

Relation

Domain

graphs that are connected lines or curves

graphs that are only distinct points

a set of ordered pairs

the set of first coordinates (x-value) of the ordered pairs

Continuous Graph

graphs that are connected lines or curves

Discrete Graph

graphs that are only distinct points

Continuous Graph

Discrete Graph

Relation

Domain

graphs that are connected lines or curves

graphs that are only distinct points

a set of ordered pairs

the set of first coordinates (x-value) of the ordered pairs

Continuous Graph

graphs that are connected lines or curves

Discrete Graph

graphs that are only distinct points

Axis of Symmetry

Complex Conjugates

Complex Number

Completing the Square

A line through a shape so that each side is a mirror image. W…

Each of two complex numbers having their real parts identical…

A number that can be expressed in the form a + bi, where a an…

A technique used to solve quadratic equations, graph quadrati…

Axis of Symmetry

A line through a shape so that each side is a mirror image. W…

Complex Conjugates

Each of two complex numbers having their real parts identical…

System of Two Linear Equations

Solution

Consistent System

Inconsistent Solution

Consists of two equations that can be written as:... Ax + By = C…

An ordered pair (x,y) that satisfies each equation in the sys…

A system that has at least one solution.

A system that has no solutions.

System of Two Linear Equations

Consists of two equations that can be written as:... Ax + By = C…

Solution

An ordered pair (x,y) that satisfies each equation in the sys…

term

literal factors

numerical coefficient

monomial

the product of letters, numbers, or both

the variables in the term

the number that is a factor

a term with only whole numbers are exponents

term

the product of letters, numbers, or both

literal factors

the variables in the term

reflexive property

symmetric property

transitive property

substitution property

a=a ex: 2/3=2/3 anything is congruent to itself

if a=b, b=a

if a=b and b=c, then a=c

if a=b then b may be substituted for a in any expression

reflexive property

a=a ex: 2/3=2/3 anything is congruent to itself

symmetric property

if a=b, b=a

linear equation

standard form

x-intercept

y-intercept

an equation that forms a line when it is graphed

Ax + By = C... "C" is called the constant. Ax + By are the varia…

the x coordinate of the point at which the graph of the equat…

the y coordinate of the point at which the graph of the equat…

linear equation

an equation that forms a line when it is graphed

standard form

Ax + By = C... "C" is called the constant. Ax + By are the varia…

Ray

Angle

Initial Side

Terminal Side

a part of a line that has only one endpoint and extends forev…

formed by two rays that have a common endpoint

one ray of an angle (x-axis)

other ray of an angle

Ray

a part of a line that has only one endpoint and extends forev…

Angle

formed by two rays that have a common endpoint

Compound Inequality:

Cross Products (of a Proportion):

Equation:

Equivalent Equations:

Two inequalities that are joined by and or "or"... Example: 5 <…

In a proportion a/b = c/d, the products ad and bc. These prod…

A mathematical sentence that uses an equal sign.... Example: x+5…

Equations that have the same solution.... Example: 9/3=3 and 9/3…

Compound Inequality:

Two inequalities that are joined by and or "or"... Example: 5 <…

Cross Products (of a Proportion):

In a proportion a/b = c/d, the products ad and bc. These prod…

inverse operation

equivalent equations

like terms

input

2 operations that undo each other: addition and subtraction,…

equations that have the same solution

expressions that contain the same variables to the same power

the x value, the domain

inverse operation

2 operations that undo each other: addition and subtraction,…

equivalent equations

equations that have the same solution

system of equations

consistent

inconsistent

independent

two or more equations with the same variables

a system of equations that has at least one solution

a system of equation that has no solutions

a consistent system that has exactly one solution

system of equations

two or more equations with the same variables

consistent

a system of equations that has at least one solution

Elimination method

System of equations

Dependent

Bounded

Eliminate one of the variable in a system of equations by add…

A set of equation with the same variables

When a system of linear equations has an infinite number of s…

A region is _____ when the graph of a system of constraints i…

Elimination method

Eliminate one of the variable in a system of equations by add…

System of equations

A set of equation with the same variables

Linear Equation

Standard Form

Linear Function

Parent Function

An equation that forms a line when it is graphed

(Ax + By = C) A≥0, Both A & B ≠ 0, A-B-C have to be integers,…

Function whose graph is a line

f(x)=x

Linear Equation

An equation that forms a line when it is graphed

Standard Form

(Ax + By = C) A≥0, Both A & B ≠ 0, A-B-C have to be integers,…

negative exponents

product of powers

quotient of powers

power of a power

move term to denominator

add exponents if bases are the same

subtract exponents if bases are the same

multiply the exponents together

negative exponents

move term to denominator

product of powers

add exponents if bases are the same

term

literal factors

numerical coefficient

monomial

the product of letters, numbers, or both ... 3... x... -17ab^2c^3d^5

the variables in the term... 7xy LF= x & y

the number that is a factor... 7xy NC=7... x^2y^3 NC=1

a term with only whole numbers as exponents... 7xy... x^2y^3

term

the product of letters, numbers, or both ... 3... x... -17ab^2c^3d^5

literal factors

the variables in the term... 7xy LF= x & y

Domain; independent variable.

Range; dependent variable.

Function.

Vertical- line test.

The first coordinate (x- coordinate).

The second coordinate (y- coordinate).

Each input (domain) is paired with exactly one output (range).

A test given to a line to determined fit is a function.

Domain; independent variable.

The first coordinate (x- coordinate).

Range; dependent variable.

The second coordinate (y- coordinate).

Factoring

Factoring x^2 + bx + c

Factoring the Difference of Two Squares

Factoring Perfect-Square Trinomials

Allows you to write the sum as a product (reverses the normal…

To factor an expression of the form ax^2 + bx + c where a=1,…

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

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

Factoring

Allows you to write the sum as a product (reverses the normal…

Factoring x^2 + bx + c

To factor an expression of the form ax^2 + bx + c where a=1,…

Monomial

Terms

Coefficient

Degree

A number, a variable, or a product of numbers and variables w…

The parts of an expresion that are seperated by addition.

A constant in the beginning of each term.

The sum you get from the exponents of the variables. A consta…

Monomial

A number, a variable, or a product of numbers and variables w…

Terms

The parts of an expresion that are seperated by addition.