The domain and range of a relation are defined as the sets of all the x-coordinates and y-coordinates of the ordered pairs, respectively. In this article, we will discuss the domain and range of a function. It represents the possible outputs that can be obtained which, in the above example, are chips and soda. Also, you cannot buy pizza from the machine no matter how much you pay. Similarly, the domain represents the inputs available for a function, just like notes. You can buy chips and soft drink cans with bill notes, but if you put in coins, the machine will reject them. They work just like a vending machine in this case. Domain and range are the most important parts of a function. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the For example, as “the set of x-values such that 10 is less than or equal to x, x, and x x is less than 30.”įigure 5 compares inequality notation, set-builder notation, and interval notation. We can also use inequalities, or other statements that might define sets of values or data, to describe the behavior of the variable in set-builder notation. In the previous examples, we used inequalities and lists to describe the domain of functions. Using Notations to Specify Domain and Range As a more extreme example, a function’s inputs and outputs can be completely different categories (for example, names of weekdays as inputs and numbers as outputs, as on an attendance chart), in such cases the domain and range have no elements in common. For example, the function f ( x ) = − 1 x f ( x ) = − 1 x has the set of all positive real numbers as its domain but the set of all negative real numbers as its range. See Figure 3 for a summary of interval notation.Ĭan there be functions in which the domain and range do not intersect at all?
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