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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:

0

2 1

5 2

2 0 2 4

    1
3

3

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

Domain:

    2
    0
    2
    3

Range:

    1
    1
    2
    3

Domain:

Range: 1

    4

Domain:

Range:

Domain:

Range:

    1
    3

Domain:

Range: 2 3

Domain:

Range:

    1
    3

Domain: 4 0

Range: 0 4

Domain:

Range: 4

Domain:

Range: 0

Domain: 0

Range:

Domain:

    3
    2
1

Range:

    0
    1
    2

Domain:

Range:

    4

Domain: 4 4

Range:

    4
    2
    0
    2

Domain: 4 4

Range: 0 4

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Source:  OpenStax, "rational"ity. OpenStax CNX. May 03, 2006 Download for free at http://cnx.org/content/col10350/1.2
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