Introduction to Domain and Range of Functions

LEARNING OBJECTIVES

By the end of this lesson, you will be able to:

  • Find the domain of a function defined by an equation
  • Write Domain and Range Using Standard Notations
  • Find Domain and Range from a Graph
  • Define Domain and Range of Toolkit Functions
  • Graph Piecewise-Defined Functions

If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions such as these.

Two graphs where the first graph is of the Top-Five Grossing Horror Movies for years 2000-2003 and Market Share of Horror Movies by Year

Figure 1. Based on data compiled by www.the-numbers.com.