Algebra 1 Vocabulary FLVS

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Rational Functions

A function that can be represented using fractions of polynomials

Linear Function

A function that is defined by a linear expression and written using function notation

Exponential Function

A function that is defined by an exponential expression and written using function notation, and the variable is an exponent; example, f(x) = abx

Scatter Plot

A graph on which two different sets of data are plotted using coordinates

Line of Best Fit

A line drawn through the points on a scatter plot to summarize the relationship between the two sets of data

Square Roots

A number times itself equals the square under the radical sign

Coefficient

A number which multiplies a variable; example: 3x, 3 is the coefficient

Absolute Value

A number's distance from zero on a number line; examples: |-3| = 3 and |3| = 3; both numbers are 3 units away from zero

Composite Function

A process in which the output of one function is the input for the next function: example: f[g(x)]

Combining Like Terms

A process of combining terms that have identical variable parts.

Completing the Square

A process that allows one to rewrite a quadratic trinomial in general form or standard form into vertex form

Zero Exponent Property

A property that says any number (except 0) with an exponent of 0 is defined to equal 1; a0 = 1

Negative Exponent Property

A property that says any number raised to a negative power equals to the reciprocal of the positive exponent of the number; a^-2=1/a^n

Rational Exponent Property

A property that says fractional powers, or where a number is raised to a fraction, can be converted to a radical; the numerator becomes the exponent, and the denominator becomes the index of the radical; x ^m/n = n square root of x^m

Zero product Property

A property that says that zero times anything equals zero. If ab = 0, then either a or b (or both) has to be zero. If a polynomial has factors multiplied together and the product is zero, then at least one of them has to be zero.

Power of a Quotient Property

A property that says to find a power of a quotient, find the power of each part of the quotient, and then divide by canceling common factors; (x/y)^n = x^n/y^n

Power of a Power Property

A property that says to raise a power to a power, multiply the exponents; (am)n = am • n

Power of a Product Property

A property that says to raise a product inside parentheses to a power, apply that power to each factor inside the parentheses; (ab)m = ambm

Vertex Form of a Quadratic Equation

A quadratic equation of the form y = a(x − h)2 + k where (h, k) is the vertex of the parabola

Standard Form of a Quadratic Equation

A quadratic equation of the form y = ax2 + bx + c, where each term is in decreasing order of degree

Relation

A relationship that pairs input values with output values

Monofilament

A single, untwisted, synthetic filament

Extraneous Solution

A solution of the simplified form of the equation that doesn't satisfy the original equation

Controlled Study

A study on two comparable groups; the groups are given different sets of experiences, and the outcomes are compared

Arithmetic Series

A sum of a list of numbers that are separated by a common difference

Geometric Series

A sum of a list of numbers that are separated by a common ratio

Variable

A symbol, usually a letter, which takes the place of an unknown value

Consistent System

A system of equations that has at least once solution; a pair of intersecting lines or same lines are consistent systems

Inconsistent System

A system of equations that has no solution is called an inconsistent system; parallel lines are an inconsistent system

Two-way Frequency Table

A table where each cell in the table has the frequencies of two categories of data

Vertical Line Test

A test that determines if the graph of something is a function—if the graph crosses any vertical line at more than one point, the relation is not a function

Correlation Coefficient

A value that describes how closely the numbers in the data set are related

Factor

A value that is multiplied by another value to get a product

Axis of Symmetry

A vertical line that passes through the vertex of the parabola

Box Plot

A visual that divides a list of data into four sections called quartiles

Bar Graph

A visual that shows data that appear in categories

Histograms

A visual that shows data that appear in ranges (numerical data)

Dot Plot

A visual that shows the frequency of which something occurs; in a dot plot, the number of dots over a number line tells how many times that number occurs in the data

Point-Slope Form

A way of writing a linear equation using the slope and any point on the line y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line

Quadratic Equation

An equation of the form y = ax2 + bx + c, where "a", "b" and "c" are real numbers, and "a" cannot be zero

Rational Equations

An equation represented using fractions of polynomials

Radical Equation

An equation that has a variable in the radicand

Literal Equations

An equation that has two or more variables

Function Rule

An equation that represents an output value in terms of an input value

Proportion

An equation that states two ratios are equal

Linear Equation

An equation whose graph is a straight line, where the highest exponent on the variables is 1

Rational Exponent

An exponent expressed as a fraction

Prime Expression

An expression that does not have a common factor in the coefficients or the variables and cannot be factored in any other way

Linear Inequalities

An inequality that can be expressed as an equation and it graphed as a line with areas of inclusion and exclusion

Perfect Square

An integer that can be made by multiplying two of the same integers together

Closure Property

An operation is considered closed over a set of numbers or a system when two or more elements of the same set are combined by that operation and the result is also an element of the set.

Sequence

An ordered list of numbers, objects, or events that often form a pattern

Term

One letter, number, or product of letters and numbers, also known as a monomial

Terms

One letter, number, or product of letters and numbers, also known as a monomial

Monomial

One letter, number, or product of letters and numbers, also known as a term

Parallel Lines

Parallel lines have the same slope, are traveling in the same direction, and will never cross, but have different y-intercepts

Nonviable

Not a possible solution to the question being asked

Inequality

Not equal, more than, less than, not the same

Function Notation

Notation that is used to represent a function; namely f(x), read f of x

Elements

Numbers or objects in a set

Consecutive Integers

Numbers right beside each other on a number line; for example: 1, 2, 3, ... or -5, -6, -7, ...

Dividend

Numerator, or what is being divided into

Consecutive Odd Integers

Odd numbers right beside each other on a number line; for example 1, 3, 5, ... or -3, -5, -7, ...

Exponent

Tells how many times the base is used as a factor, or the number of time the base is multiplied by itself

Like Terms

Terms with the exact same variables with the exact same exponents for the variables

End Behavior

The behavior of the graph of as x approaches positive infinity or negative infinity

Run

The horizontal change of a line from one point to another

Rate (interest)

The interest rate you are given on the money you borrow

Intersection

The intersection of two or more sets is made up of the elements that the sets share; the term intersection is represented using an upside down symbol which looks like ∩

Greatest Common Factor (GCF)

The largest positive integer that divides without a remainder into two or more chosen integers

Maximum (of data set)

The largest value in a data set

Boundary Lines

The line in the graph of an inequality that divides the plane into two parts—one side representing points that are solutions to the inequality and one side representing points that are not solutions to the inequality; the lines are dashed or solid based on the inequality symbol

Central Tendency

The measure of the "middle" of a set of data; common measures are the arithmetic mean, median, and mode

Interquartile Range (IQR)

The middle half of the data; it is a measure of how widely the middle half of the data is spread around the median

First Quartile

The midpoint of the lower half of the data when the data is listed in numerical order

Lower Quartile

The midpoint of the lower half of the data when the data is listed in numerical order; also known as the first quartile

Reciprocal

The multiplicative inverse of a number; for example, 2 divided by 3 is the reciprocal of 3 divided by 2

Radicand

The number or expression contained under a radical sign

Base

The number or quantity being raised to a power

Median

The number that falls in the middle when the data are ordered; when there is an odd number of terms, it is the middle term; when there is an even number of terms, it is the mean of the two middle terms

Exponential Decay

When the graph of an exponential function decreases from left to right; the base of the exponential expression must be between 0 and 1

Exponential Growth

When the graph of an exponential function increases from left to right; the base of the exponential expression must be greater than 1

Compound Interest

When the interest rate (or rate of growth) is applied to the principal and all other interests earned to that point

Simple Interest

When the interest rate (or rate of growth) is applied to the principal only

Algebraic Ratio

When the numerator, denominator, or both parts of a ratio contains a variable expression

Standard Form

When the polynomial is listed with each term in decreasing order of degree

Independent System

When two lines do not share all of the same points, such as parallel lines or intersecting lines

Intercept

Where the line you are graphing intersects the axes of the coordinate plane

Law of Negative Exponents

a-n = 1/a^n . The multiplicative inverse of the base raised to the positive opposite of the power.

Product of Powers Property

am • an = am+n. To multiply powers with like bases, add the exponents.

Probability

How likely an event is to occur

Real Number

A number that is rational or irrational; examples: -4, , 1/3, 3.2

Horizontal Lines

Lines that have a slope equal to zero

Vertical Lines

Lines that have a slope that in undefined

Rise

The vertical change of a line from one point to another

Compound Inequality

Two inequalities joined by the word "and" or the word "or"

Difference of Two Squares

Two perfect squares being subtracted

PEMDAS

"Please Excuse My Dear Aunt Sally" is a mnemonic device reminding you that the order of operations is Parentheses, Exponents, Multiplication or Division, and finally Addition or Subtraction

Explicit Formulas

A formula that can generate any term in a sequence just by inputting the term number

Recursive Formula

A formula that can generate terms one at a time by relating the term to one or more previous terms

Rational Expression

A fraction containing polynomials

Equal Sign

=; Tells you that what is on the left side of the equation equals what is on the right side of the equation

Inequality Symbols

> greater than, < less than, ≥ greater than or equal to, ≤ less than or equal to

Parabola

A U-shaped curve, created by a quadratic equation

Statistics

A branch of mathematics that views numbers as data sets and teaches how to use a variety of methods to organize, interpret, and analyze these numbers to make informed decisions

Set

A collection of numbers or objects

Ratio

A comparison of two numbers by division

Constant Function

A constant function is a linear function of the form y = b, where b is a constant; it is also written as f(x) = b; the graph of a constant function is a horizontal line

Outlier

A data point that is significantly larger or smaller than the other values

Standard Form of a Linear Equation

A linear equation in which the x term and the y term are written on the same side of the equal sign, with the constant (number-only term) on the other side; A, B, and C are integers; and A is positive; Ax + By = C

Arithmetic Sequence

A list of terms that share a common difference; the difference between the consecutive terms is constant

Geometric Sequence

A list of terms that share a common ratio; each term is found by multiplying or dividing the same value from one term to the next

Polynomials

A mathematical expression that has: a) one or more terms, b) variables with only positive, whole number exponents, and c) no variables in the denominators of each term

Function

A mathematical relationship in which each input value is paired with exactly one output value

Equation

A mathematical statement containing an equal sign to show that two expressions are equal

Standard Deviation

A measure of spread to allow for comparisons to the overall data set; found by finding the sum of the square of the differences of each data point from the mean, dividing it by the number of data points, and square rooting that value

Sigma Notation

A method of writing a long series of numbers in an abbreviated format; also known as summation notation

Numerical Expression

A number or a group of numbers that are added, subtracted, multiplied, or divided; example: 4 + 6 is a numerical expression

Rational Number

A number that can be expressed as a ratio (fraction) of two numbers; this includes decimals that terminate or repeat; examples: , 4/5 -14, 2.1, √4 (square root of 4 is 2, and is rational)

Irrational Number

A number that cannot be expressed as a ratio (fraction) of two numbers; this includes decimals that never stop or repeat; examples: √5, 3.2516...

Slope-Intercept Form

A way of writing a linear equation where the y-variable is isolated on one side of the equation. Slope-intercept looks like y = mx + b, where m equals the slope and b equals the y-intercept.

The Statistical Process

A way to collect, organize, understand, and represent data; a standardized process so that analysis can be compared and informed decisions can be made using comparable data

Whole Number

All positive whole numbers including zero; this category does not include any negative whole numbers; examples: 0, 3, 6

Natural Number

All positive whole numbers, not including zero; examples: 4, 7, 9

Algebraic Equation

An algebraic equation is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc. and also contains an equal sign that sets two algebraic expressions equal to each other; example: x + 4 = 9 is an algebraic equation

Algebraic Expression

An algebraic expression is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc; example: x + 4 is an algebraic expression

Quotient

Answer to the division problem

Infinitely Many Solutions

Any ordered pair that satisfies one of the equations or inequalities will also satisfy the other equation or inequality; the equations describe the same line, or the inequality has the same border line

Reflexive Property

Anything is equal to itself; same numbers or terms on both sides of the equal sign, 5 = 5

Mondrian Art

Art that uses vertical and horizontal lines with geometric fields of colors

Prime Factorization

Factoring a number into its prime factors only

System of Equation

Collection of two or more equations

Nonlinear System of Equations

Collection of two or more equations where at least one equation is not linear

Divisor

Denominator, or what is being divided by

Transformation

Describes the change in a figure

Graphical Representation

Displaying an equation, point, or segment on a graph

Simplify

Distributing, combining like terms, etc.

Term of a sequence

Each individual number, object, or event in a list of a sequence is called a term

Elimination Method

Eliminating one of the variables when combining the two equations

Rationalizing the Denominator

Eliminating the square root (radical) from the denominator

Degree of a Polynomial

Equal to the degree of the term with the highest degree

Consecutive Even Integers

Even numbers right beside each other on a number line; for example 2, 4, 6, ... or -4, -6, -8, ...

Infinite

Extending to infinity or indefinitely

Cross Multiply

Finding the cross products of two ratios

Greatest Perfect Square Method

Finding the largest perfect square factor of a number or expression that is not a perfect square

Transitive Property

For any real numbers a, b, and c if a = b, and b = c, then a = c. Three parts: the first statement relates to the second, which relates to the third.

Distributive Property

For every real number a, b, and c, a(b + c) = ab + ac or a(b - c) = ab - ac

Addition Property of Equality

For every real number a, b, and c, if a = b then a + c = b + c

Multiplication Property of Equality

For every real number a, b, and c, if a = b then a(c) = b(c)

Subtraction Property of Equality

For every real number a, b, and c, if a = b, then a - c = b - c

Division Property of Equality

For every real number a, b, and c, if a = b, then a ÷ c = b ÷ c

Inverse Functions

Functions whose compositions simplify to x; for example, if f(x) and g(x) are inverses of each other, then f(g(x)) = g(f(x)) = x

Associative Property of Addition or Multiplication

Grouping symbols do not affect the outcome. Numbers can be associated by using parentheses or brackets in an addition or multiplication problem and it does not change the solution.

Factoring by Grouping

Grouping terms into pairs before factoring a GCF from each group

Guess and Check Method

Guess a solution and check to see if it works by substituting it into the equation

Accuracy

How closely a given set of values are compared to the expected value

Substitution

If two quantities are equal, one quantity may be put in the place of the other quantity and the value of the expression does not change

Carbon Footprint

Impact on the environment

Leading Coefficient

In a polynomial in terms of x, the coefficient in front of the x term with the highest degree in the polynomial

Conjunction

Inequalities joined by the word "and"

Disjunction

Inequalities joined by the word "or"

Horizontal Asymptote

Invisible horizontal lines that a rational function approaches, yet does not cross, when graphed

Vertical Asymptote

Invisible vertical lines that a rational function approaches, yet does not cross, when graphed

Substitution Method

Isolating one variable in one of the equations and substituting it into the other equation

Opposite Operation

Performing the inverse operation to solve an equation; example: the inverse of addition is subtraction; the inverse of multiplication is division

Perpendicular Lines

Perpendicular lines have opposite reciprocal slopes and always cross at a 90o angle; for example, a line having slope 2 is perpendicular to a line having slope -1/2

Integer

Positive and negative whole numbers including zeros; this category does not include any fractions or decimals; examples: -2, 0, 4

Viable

Possible solution to the question being asked

Mono-

Prefix for words involving only one thing

Tri-

Prefix for words involving three things

Bi-

Prefix for words involving two things

Absolute Value Inequalities

Problems that involve ranges with inequalities

Properties of Equality

Properties that state that two or more items are the same

Real Number System

System of numbers that includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers

Equivalent Systems

Systems of equations that have the same solutions

Constraints

Restrictions placed on a variable depending on a real-world situation

Mean Absolute Deviation

Shows the average distance of the data points from the mean; f found by finding the sum of the differences of each data point from the mean and dividing it by the number of data points

Joint Frequency

Shows the data for each two-category response and occurs in the body of the table; found by reading from the inner cells of a two-way frequency table

Restriction

Stating that a variable cannot equal a specific number or set of numbers

Grouping Symbols

Symbols that signify two or more things are grouped together; parentheses ( ) or brackets [ ]

Parameter

The constant or the limits within the problem

Residuals

The difference between the actual values and the predicted values; normally used to determine the accuracy of the line of best fit created on a scatter plot

Range (of data set)

The difference between the largest and smallest values in a data set

Difference

The difference between two numbers (subtraction)

Rate of Change, or Slope

The difference of the y-values divided by the difference of the x-values

Slope

The difference of the y-values divided by the difference of the x-values

Discriminant

The expression located under the radical in the Quadratic Formula that can determine the number and type of solutions to a quadratic equation

Perfect Square Trinomial

The first and last terms of a trinomial are perfect squares and the middle term is equal to two times the product of the square roots of the first and last terms

Order of Operations

The order in which mathematical operations should be done: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).

Commutative Property of Addition or Multiplication

The order in which you perform an operation does not affect the outcome. Numbers can move around or commute in an addition or multiplication problem and it does not change the solution.

Symmetric Property

The order on either side of the equal sign does not matter. One side of the equation is the same as the other (think symmetrical) 3 = 2 + 1, 2 + 1 = 3

Principal

The original amount you borrow

Parent Function

The original function or function you start with

Solution to a System of Equations

The pair of values that make both equations true

X-Intercept

The point where a graph intersects the x-axis; the value of x when y = 0

Y-intercept

The point where a line crosses the y-axis; the value of y when x = 0

Domain

The possible input values (x values)

Range

The possible output values (y-values)

Function Composition

The process of combining two functions by using the output of one function as the input in the second function

Joint Relative Frequency

The proportional values found in the interior of a relative frequency table

Slope of a Line

The ratio of the vertical change to the horizontal change between two points, represented in equations by m

Correlation

The relationship between two groups of data

Sum

The result of adding

Equality

The same

Negative Slope

The slope of a line is negative if the line runs from the top left to the bottom right; the moves for the slope should be opposite moves, either down and to the right or up and to the left

Positive Slope

The slope of a line is positive if the line runs from the bottom left to the top right; the moves for the slope should be either both in the positive direction (up and to the right) or both in the negative direction (down and to the left)

Undefined Slope

The slope of a vertical line

Least Common Multiple (LCM)

The smallest (least) multiple that the two numbers have in common (the same). Example, the LCM of 2 and 3: Multiples of 2 are 2, 4, 6, 8, 10, 12, etc. Multiples of 3 are 3, 6, 9, 12, 15, etc. The smallest multiple they have in common is 6.

Minimum (of data set)

The smallest value in a data set

Area

The space surface takes up, measured in square units

Quotient Property of Radicals

The square root of a quotient is equal to the quotient of the square roots.

Mean

The sum of the data points divided by the number of data points

Degree of a Term

The sum of the exponents on the variables in the term

Trinomial

The sum or difference of three terms

Binomial

The sum or difference of two terms

Radical

The symbol for a square root

Vertex

The turning point (minimum or maximum) of a parabola

Solution

The value for the variable that makes the equation true

Power

The value of a number or quantity raised to some exponent

Relative Frequency

The value of each cell shown as a ratio with respect to all of the data in a two-way frequency table; shows each frequency as a proportion of the whole data sample size

Average Rate of Change

The value that shows how much the range values have changed per unit in the domain for a specified interval in the domain

Marginal Frequency

The values calculated from the row and column totals in a two-way frequency table

Zeros of a Polynomial

The values of the input of a polynomial function that would make the function zero; appear as the x-intercepts on the graph of the polynomial

Marginal Relative Frequency

The values shown in the column and row totals of a relative frequency table

Maximum Point

The vertex of a parabola that opens down

Minimum Point

The vertex of a parabola that opens up

Upper Quartile

This is the midpoint of the upper half of the data when the data are listed in numerical order; also known as the third quartile

Third Quartile

This is the midpoint of the upper half of the data when the data is listed in numerical order

Conditional Relative Frequency

This value shows a frequency proportion for a given condition or category

Evaluate

To calculate the value of

Distribute

To deliver or pass something out

Expanded Form of an Exponent

To expand a power means to write the multiplication represented by the exponent

Least Common Denominator (LCD)

To find a Least Common Denominator (LCD), start by listing the first few multiples of each denominator. Stop when you find a multiple that they have in common. This is the LCD.

Associate

To group with something else

Commute

To move around

Transit

To move something around

Reflection

To see the exact opposite of something, like the reflection in a mirror

Isolate

To separate out from all other parts

Closed Circle

Used on number lines when graphing greater than or equal to or less than or equal to inequalities

Open Circle

Used on number lines when graphing greater than or less than inequalities

All Real Numbers

Used when solving an equation in which both sides of the equation are the same; all real numbers means that any real number would make the equation true

No Solution

Used when solving an equation or inequality in which the solution is false; no solution means that there is no possible value for x that would make the equation or inequality true

Prime

When a number can be evenly divided only by one and itself

Dependent System

When all of the solutions on one line are the same as the other line in a system; this would create the same line

Descending Order

When all of the solutions on one line are the same as the other line in a system; this would create the same line

Causation

When one set of data directly causes the other to occur

Rate

When one unit of measure changes in terms of another unit


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