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# Using Interval Notation

Module by: Pradnya Bhawalkar, Kim Johnston. E-mail the authors

Summary: An introductory explanation on how to use interval notation (versus set notation)

Interval notation is another method for writing domain and range.

In set builder notation braces (curly parentheses {} ) and variables are used to express the domain and range. Interval notation is often considered more efficient.

In interval notation, there are only 5 symbols to know:

• Open parentheses ( )
• Closed parentheses [ ]
• Infinity
• Negative Infinity
• Union Sign

To use interval notation:

Use the open parentheses ( ) if the value is not included in the graph. (i.e. the graph is undefined at that point... there's a hole or asymptote, or a jump)

If the graph goes on forever to the left, the domain will start with ( . If the graph travels downward forever, the range will start with ( . Similarly, if the graph goes on forever at the right or up, end with )

Use the brackets [ ] if the value is part of the graph.

Whenever there is a break in the graph, write the interval up to the point. Then write another interval for the section of the graph after that part. Put a union sign between each interval to "join" them together.

Now for some practice so you can see if any of this makes sense.

Write the following using interval notation:

## Exercise 6

Write the domain and range of the following in interval notation:

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