Chapter 3: Graphing Linear Functions

Comprehensive vocabulary flashcards covering relations, functions, domain and range, linear vs. nonlinear functions, discrete and continuous domains, and function notation.

Relation

A pairing of inputs with outputs.

Function

A relation that pairs each input with exactly one output.

Domain

The set of all possible input values for a relation or function.

Range

The set of all possible output values for a relation or function.

Independent Variable

The variable that represents the input values of a function because it can be any value in the domain.

Dependent Variable

The variable that represents the output values of a function because it depends on the value of the independent variable.

"$y$ is a function of $x$"

A mathematical statement meaning that the dependent variable $y$ varies depending on the value of the independent variable $x$.

Vertical Line Test

A visual method stating that a graph represents a function when no vertical line passes through more than one point on the graph.

Linear Equation in Two Variables

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

Linear Function

A function whose graph is a nonvertical line, which has a constant rate of change and can be represented by a linear equation in two variables.

Nonlinear Function

A function that does not have a constant rate of change, resulting in a graph that is not a line.

Constant Rate of Change

A property describing a quantity that changes by equal amounts over equal intervals.

Solution of a Linear Equation in Two Variables

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

Graph of a Linear Equation in Two Variables

The set of all points $(x, y)$ in a coordinate plane that represent solutions of the equation.

Discrete Domain

A set of input values that consists of only certain numbers in an interval, such as distinct integers.

Continuous Domain

A set of input values that consists of all numbers in an interval, including fractions and decimals.

Default Domain of a Linear Function

The understanding that when the domain of a linear function is not specified or obtained from a real-life context, it is all real numbers.

Representations of Functions

The five standard ways to describe a function: using words, an equation, an input-output table, a mapping diagram, and a graph.

Function Notation

A method of writing a function where $y$ is replaced by $f(x)$, read as "the value of $f$ at $x$" or "$f$ of $x$," representing the output corresponding to the input $x$.

$x$-intercept

The $x$-coordinate of a point where a graph crosses the $x$-axis, found by substituting $0$ for $y$ and solving for $x$.

$y$-intercept

The $y$-coordinate of a point where a graph crosses the $y$-axis, found by substituting $0$ for $x$ and solving for $y$.