Chapter 1 Outlines: Functions, Representations, and Models

Function

A rule that assigns to every input in its domain exactly one output.

Domain

The set of all input values (x-values) for which a function is defined.

Range

The set of all possible outputs (f(x)) produced by the function.

Verbal representation

Describing a function’s relation in words rather than symbols.

Algebraic representation

A function described by a formula, such as f(x) = 2x + 3.

Graph

A plotted representation of the relationship on a coordinate plane, with input on the x-axis and output on the y-axis.

Table of values

A tabular listing of input-output pairs used to illustrate how a function behaves at selected points.

Vertical Line Test

A test to determine if a relation is a function by ensuring each vertical line intersects the graph at most once.

Increasing function

A function that grows as the input increases: f(x1) < f(x2) whenever x1 < x2 on the interval.

Decreasing function

A function that falls as the input increases: f(x1) > f(x2) whenever x1 < x2 on the interval.

Piecewise defined function

A function defined