Overview
On this page, we discuss the domain and range of a function, and how to find them.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Be comfortable using the English notation for intervals: \([a,b]\) for the interval including the endpoints (a “closed interval”), \((a,b)\) for the interval excluding the endpoints (an “open interval”), and the mixed cases like \([a,b)\) or \((a,b]\).
- Read off the domain and range from the given graph of a function.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Identify the domain of a function given in formula form, in particular for functions involving a fraction or roots.
To prepare for class
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Use (at least some of) the videos on the following page to review interval notation (this is in particular important for francophone students, as you’ll have to get used to the English notation for intervals!): Sec IV: Inequalities and Interval Notation
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Watch the following videos (by Mathispower4u, 4m48s, and Mario’s Math Tutoring, 4m24s, respectively) which explain how to read off the domain and range of a function (or relation) from a given graph::
After class
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Watch the following video (by Tyler Wallace) which explains how to determine the domain of a function which is given only in formula form, in particular for functions involving a fraction or a root:
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Watch the following video (by NancyPi) which shows in detail how to find the domain of some of the most important types of functions you might encounter:
