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Using Interval Notation

Module by: Pradnya Bhawalkar, Kim Johnston

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:
Problem 1
Figure 1
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Solution 1
0 0
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Problem 2
Figure 2
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Solution 2
--21 2 1
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Problem 3
Figure 3
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Solution 3
-52 5 2
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Problem 4
Figure 4
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Solution 4
--2024 2 0 2 4
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Problem 5
Figure 5
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Solution 5
-13 1 3
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Problem 6
Figure 6
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Solution 6
-3 3
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Write the domain and range of the following in interval notation:
Problem 7
Figure 7
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Solution 7
Domain: -2023 2 0 2 3
Range: -1123 1 1 2 3
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Problem 8
Figure 8
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Solution 8
Domain: -
Range: 14 1 4
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Problem 9
Figure 9
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Solution 9
Domain: -
Range: -
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Problem 10
Figure 10
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Solution 10
Domain: -
Range: 13 1 3
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Problem 11
Figure 11
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Solution 11
Domain: -
Range: -23 2 3
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Problem 12
Figure 12
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Solution 12
Domain: -
Range: 13 1 3
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Problem 13
Figure 13
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Solution 13
Domain: -40 4 0
Range: 04 0 4
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Problem 14
Figure 14
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Solution 14
Domain: -
Range: -4 4
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Problem 15
Figure 15
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Solution 15
Domain: -
Range: 0 0
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Problem 16
Figure 16
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Solution 16
Domain: 0 0
Range: -
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Problem 17
Figure 17
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Solution 17
Domain: -3-2-1 3 2 1
Range: 012 0 1 2
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Problem 18
Figure 18
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Solution 18
Domain: -
Range: 4 4
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Problem 19
Figure 19
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Solution 19
Domain: -44 4 4
Range: -4-202 4 2 0 2
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Problem 20
Figure 20
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Solution 20
Domain: -44 4 4
Range: 04 0 4
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