Chapter 2

2.1 Functions

Overview

Objectives

1. Define the terms function, domain and range.
2. Use function notation to evaluate functions at given values.
3. Define the graph of a function and apply the vertical line test.
4. Find the domain and range of a function by using its graph.
5. Understand the relationship between the formula for a function and its graph.

Examples and Definitions

A function is a rule that has exactly one output for each input. The set of valid inputs if the domain of the function and the corresponding set of outputs is the range of the function.

The graph of a function f is the set of all points (x, y) with y=f(x).

An equation defines y as a function of x if and only if no vertical line crosses the graph of the equation more than once.

Example 1

Find the domain of the function

Positive numbers and the number zero have real square roots. The domain of the function is the set of all .

Example 2

Given , find