Connexions

You are here: Home » Content » Using Interval Notation
Content Actions

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
[ Click for Solution 1 ]
Solution 1
0∞ 0
[ Hide Solution 1 ]
Problem 2
Figure 2
[ Click for Solution 2 ]
Solution 2
-∞-2⋃1∞ 2 1
[ Hide Solution 2 ]
Problem 3
Figure 3
[ Click for Solution 3 ]
Solution 3
-52 5 2
[ Hide Solution 3 ]
Problem 4
Figure 4
[ Click for Solution 4 ]
Solution 4
-∞-2⋃02⋃4∞ 2 0 2 4
[ Hide Solution 4 ]
Problem 5
Figure 5
[ Click for Solution 5 ]
Solution 5
-1⋃3∞ 1 3
[ Hide Solution 5 ]
Problem 6
Figure 6
[ Click for Solution 6 ]
Solution 6
-∞3 3
[ Hide Solution 6 ]
Write the domain and range of the following in interval notation:
Problem 7
Figure 7
[ Click for Solution 7 ]
Solution 7
Domain: -2⋃0⋃2⋃3 2 0 2 3
Range: -1⋃1⋃2⋃3 1 1 2 3
[ Hide Solution 7 ]
Problem 8
Figure 8
[ Click for Solution 8 ]
Solution 8
Domain: -∞∞
Range: ∞1⋃4 1 4
[ Hide Solution 8 ]
Problem 9
Figure 9
[ Click for Solution 9 ]
Solution 9
Domain: -∞∞
Range: -∞∞
[ Hide Solution 9 ]
Problem 10
Figure 10
[ Click for Solution 10 ]
Solution 10
Domain: -∞∞
Range: 1⋃3 1 3
[ Hide Solution 10 ]
Problem 11
Figure 11
[ Click for Solution 11 ]
Solution 11
Domain: -∞∞
Range: -23 2 3
[ Hide Solution 11 ]
Problem 12
Figure 12
[ Click for Solution 12 ]
Solution 12
Domain: -∞∞
Range: 1⋃3 1 3
[ Hide Solution 12 ]
Problem 13
Figure 13
[ Click for Solution 13 ]
Solution 13
Domain: -40 4 0
Range: 04 0 4
[ Hide Solution 13 ]
Problem 14
Figure 14
[ Click for Solution 14 ]
Solution 14
Domain: -∞∞
Range: -∞4 4
[ Hide Solution 14 ]
Problem 15
Figure 15
[ Click for Solution 15 ]
Solution 15
Domain: -∞∞
Range: 0∞ 0
[ Hide Solution 15 ]
Problem 16
Figure 16
[ Click for Solution 16 ]
Solution 16
Domain: 0∞ 0
Range: -∞∞
[ Hide Solution 16 ]
Problem 17
Figure 17
[ Click for Solution 17 ]
Solution 17
Domain: -3⋃-2⋃-1∞ 3 2 1
Range: 0⋃1⋃2 0 1 2
[ Hide Solution 17 ]
Problem 18
Figure 18
[ Click for Solution 18 ]
Solution 18
Domain: -∞∞
Range: 4 4
[ Hide Solution 18 ]
Problem 19
Figure 19
[ Click for Solution 19 ]
Solution 19
Domain: -44 4 4
Range: -4⋃-2⋃0⋃2 4 2 0 2
[ Hide Solution 19 ]
Problem 20
Figure 20
[ Click for Solution 20 ]
Solution 20
Domain: -44 4 4
Range: 04 0 4
[ Hide Solution 20 ]

Comments, questions, feedback, criticisms?

Discussion forum

Send feedback