Ch. 3 Linear Functions Vocabulary Terms

Linear Equation in Two Variables

A linear equation in two variables, x and y, is an equation that can be written in the form y = mx + b, where m and b are constants. The graph of a linear equation is a line.

Linear Function

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

Nonlinear Function

A nonlinear function does not have a constant rate of change. So, its graph is not a line.

Relation

A relation pairs inputs with outputs. When a relation is given as ordered pairs, the x-coordinates are inputs and the y-coordinates are outputs.

Function

A relation that pairs each input with exactly one output is a function.

Domain

The domain of a function is the set of all possible input values.

Output Values

y values, dependent variable values, range values

Continuous Domain

A continuous domain is a set of input values that consists of all numbers in an interval. Example: All numbers from 1 to 5

Discrete Domain

A discrete domain is a set of input values that consists of only certain numbers in an interval. Example: Integers from 1 to 5

Solution of an Equation in Two Variables

A solution of a linear equation in two variables is an ordered pair (x,y) that makes the equation true. The graph of a linear equation in two variables is the set of points (x,y) in a coordinate plane that represents all solutions of the equation. Sometimes the points are distinct, and other times the points are connected.

Range

The range of a function is the set of all possible output values.

Independent Variable

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

Dependent Variable

The variable that represents the output values of a function is the dependent variable because it depends on the value of the independent variable. When an equation represents a function, the dependent variable is defined in terms of the independent variable. The statement "y is a function of x" means that y varies depending on the value of x.

Input Values

x values, independent variable values, domain values