Finding the Domain of a Function Defined by an Equation
buttons.Learning Objectives
When we purchase something from a retailer, we want to know what kind of payment they will accept. Some online retailers will accept a credit card, but not Paypal. Similarly, with functions, we cannot always assume that we can evaluate a function using any number, such as x. For example, what if you are working with the function f(x) = 1/x and you try to evaluate the function at x = 0? Recall that you cannot divide by zero, so we must let the user know that x cannot be zero, much like the retailer letting customers know what kind of payment they accept. The set of values that can be used for x in a given function is called the domain, and the resulting values that will be output from the function are called the range. In this section and all sections in this subunit, we will find the domain of a function and express it in many ways.
In this section, you will:
- Find the domain of a function defined by an equation.
- 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.
Figure 1 Based on data compiled by www.the-numbers.com.
Source: Rice University, https://openstax.org/books/college-algebra/pages/3-2-domain-and-range
This work is licensed under a Creative Commons Attribution 4.0 License.