Big Ideas Math Algebra 1 Vocabulary

These flashcards cover algebra 1 vocabulary, concepts, and formulas based on the Big Ideas Math lecture notes and glossary.

absolute value equation

An equation that contains an absolute value expression.

conjecture

An unproven statement about a general mathematical concept.

equation

A statement that two expressions are equal.

equivalent equations

Equations that have the same solution(s).

2x = 8 and 2x - 8 = 0

extraneous solution

An apparent solution that must be rejected because it does not satisfy the original equation.

formula

A literal equation that shows how one variable is related to one or more other variables.

d = rt

identity

An equation that is true for all values of the variable.

2(x+1) = 2x+2

inverse operations

Two operations that undo each other, such as addition and subtraction.

linear equation in one variable

An equation that can be written in the form $ax + b = 0$, where $a$ and $b$ are constants and $a \neq 0$.

literal equation

An equation that has two or more variables.

rule

A proven statement about a general mathematical concept; also known as a theorem.

solution of an equation

A value that makes an equation true.

theorem

A proven statement about a general mathematical concept.

absolute deviation

The absolute value of the difference of a number $x$ and a given value.

absolute value inequality

An inequality that contains an absolute value expression.

compound inequality

An inequality formed by joining two inequalities with the word 'and' or the word 'or'.

equivalent inequalities

Inequalities that have the same solutions.

graph of an inequality

A graph that shows the solution set of an inequality on a number line.

inequality

A mathematical sentence that compares expressions.

solution of an inequality

A value that makes an inequality true.

solution set

The set of all solutions of an inequality.

absolute value function

A function that contains an absolute value expression.

constant function

A linear equation written in the form $y = 0x + b$, or $y = b$.

continuous domain

A set of input values that consist of all numbers in an interval.

dependent variable

The variable that represents output values of a function.

discrete domain

A set of input values that consists of only certain numbers in an interval.

domain

The set of all possible input values of a function.

family of functions

A group of functions with similar characteristics.

function

A relation that pairs each input with exactly one output.

function notation

Another name for $y$ denoted as $f(x)$ and read as 'the value of $f$ at $x$' or '$f$ of $x$'.

horizontal shrink

A transformation that causes the graph of a function to shrink toward the $y$-axis when all the $x$-coordinates are multiplied by a factor $a$, where $a > 1$.

horizontal stretch

A transformation that causes the graph of a function to stretch away from the $y$-axis when all the $x$-coordinates are multiplied by a factor $a$, where $0 < a < 1$.

independent variable

The variable that represents the input values of a function.

linear equation in two variables

An equation that can be written in the form $y = mx + b$, where $m$ and $b$ are constants.

linear function

A function whose graph is a nonvertical line.

nonlinear function

A function that does not have a constant rate of change and whose graph is not a line.

parent function

The most basic function in a family of functions.

range of a function

The set of all possible output values of a function.

reflection

A transformation that flips a graph over a line called the line of reflection.

relation

A pairing of inputs with outputs.

rise

The change in $y$ between any two points on a line.

run

The change in $x$ between any two points on a line.

slope

The rate of change between any two points on a line.

slope-intercept form

A linear equation written in the form $y = mx + b$.

solution of a linear equation in two variables

An ordered pair $(x, y)$ that makes an equation true.

standard form of a linear equation

A linear equation written in the form $Ax + By = C$, where $A$, $B$, and $C$ are real numbers and $A$ and $B$ are not both zero.

transformation

A change in the size, shape, position, or orientation of a graph.

translation

A transformation that shifts a graph horizontally and/or vertically but does not change the size, shape, or orientation of the graph.

vertex

The point where a graph changes direction.

vertex form of an absolute value function

An absolute value function written in the form $f(x) = a|x - h| + k$, where $a \neq 0$.

vertical shrink

A transformation that causes the graph of a function to shrink toward the $x$-axis when all the $y$-coordinates are multiplied by a factor $a$, where $0 < a < 1$.

vertical stretch

A transformation that causes the graph of a function to stretch away from the $x$-axis when all the $y$-coordinates are multiplied by a factor $a$, where $a > 1$.

x-intercept

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

y-intercept

The $y$-coordinate of a point where the graph crosses the $y$-axis.

arithmetic sequence

An ordered list of numbers in which the difference between each pair of consecutive terms is the same.

causation

When a change in one variable causes a change in another variable.

common difference

The difference between each pair of consecutive terms in an arithmetic sequence.

correlation

A relationship between data sets.

correlation coefficient

A number $r$ from $-1$ to $1$ that tells how closely the equation of the line of best fit models the data.

extrapolation

To predict a value outside the range of known values using a graph or its equation.

interpolation

To approximate a value between two known values using a graph or its equation.

line of best fit

A line that best models a set of data.

line of fit

A line drawn on a scatter plot that is close to most of the data points.

linear model

A linear function that models a real-life situation.

linear regression

A method that graphing calculators use to find a precise line of fit that models a set of data.

parallel lines

Two lines in the same plane that never intersect.

perpendicular lines

Two lines in the same plane that intersect to form right angles.

piecewise function

A function defined by two or more equations.

point-slope form

A linear equation written in the form $y - y_{1} = m(x - x_{1})$.

residual

The difference of the $y$-value of a data point and the corresponding $y$-value found using the line of fit.

scatter plot

A graph that shows the relationship between two data sets.

sequence

An ordered list of numbers.

step function

A piecewise function defined by a constant value over each part of its domain.

terms of a sequence

Each number in a sequence.

graph of a linear inequality

The graph in two variables that shows all the solutions of the inequality in a coordinate plane.

graph of a system of linear inequalities

The graph of all the solutions of the system of linear inequalities.

half-planes

Two regions of the coordinate plane divided by a boundary line.

linear inequality in two variables

An inequality written in the form $ax + by < c$, $ax + by \leq c$, $ax + by > c$, or $ax + by \geq c$, where $a$, $b$, and $c$ are real numbers.

solution of a linear inequality in two variables

An ordered pair $(x, y)$ that makes an inequality true.

solution of a system of linear equations

An ordered pair that is a solution of each equation in the system.

solution of a system of linear inequalities

An ordered pair that is a solution of each inequality in the system.

system of linear equations

A set of two or more linear equations in the same variable.

system of linear inequalities

A set of two or more linear inequalities in the same variables.

common ratio

The ratio between each pair of consecutive terms in a geometric sequence.

compound interest

The interest earned on the principle and on previously earned interest.

explicit rule

A rule to define arithmetic and geometric sequences that gives $a_{n}$ as a function of the term's position number $n$ in the sequence.

exponential decay

When a quantity decreases by the same factor over equal intervals of time.

exponential decay function

A function of the form $y = a(1 - r)^{t}$, where $a > 0$ and $0 < r < 1$.

exponential equation

An equation in which variable expressions occur as exponents.

exponential function

A nonlinear function of the form $y = ab^{x}$, where $a \neq 0$, $b \neq 1$, and $b > 0$.

exponential growth

When a quantity increases by the same factor over equal intervals of time.

exponential growth function

A function of the form $y = a(1 + r)^{t}$, where $a > 0$ and $r > 0$.

geometric sequence

An ordered list of numbers in which the ratio between each pair of consecutive terms is the same.

index of a radical

The value of $n$ in the radical $\sqrt[n]{a}$.

nth root of a radical

For an integer $n$ greater than 1, if $b^{n} = a$, then $b$ is an nth root of $a$.

recursive rule

A rule to define arithmetic and geometric sequences that gives the beginning term(s) of a sequence and a recursive equation that tells how $a_{n}$ is related to one or more preceding terms.

binomial

A polynomial with two terms.

closed

When an operation performed on any two numbers in the set results in a number that is also in the set.

degree of a monomial

The sum of the exponents of the variables in the monomial.

degree of a polynomial

The greatest degree of the terms in a polynomial.