1. Interval Notation
Interval notation is a mathematical notation designed to describe a set of real
numbers. It is another way to write the domain or range of a relation.
In previous math courses, you have used set notation to describe a set of real
numbers.
Examples:
1. The set of real numbers greater than 2 is written in set notation as {x > 2}
and can be sketched on a number line as:
2 Note the open dot at 2.
This means that we don't include the
number 2 in the set.
2. The set { 5 ≤ x < 3} describes the set of real numbers between 5 and 3,
and includes the endpoint 5 in the set.
On a number line, this can be sketched as:
5 3
Note the closed dot at 5 and the open dot at 3
This means that we include the number 5 in the
set, but don't include the 3.
In interval notation, the set {x > 2} is written in the form (2,∞).
The round parenthesis indicates that we do not include the 2 in the set.
We always have a round parenthesis at ∞ or ∞.
The set { 5 ≤ x < 3} is written as [5,3) in interval notation.
The square parenthesis indicates that we include the endpoint 5 in the set.
Round parentheses correspond to open dots on sign diagrams, and square
parentheses correspond to the solid dots.
We use the notation (∞,∞) to indicate the set of all real numbers, or R.
Here are some more examples:
Set Notation Interval Notation
{ x ≤ 4} (∞,4]
{2 < x ≤ 6} (2,6]
{3 ≤ x ≤ 0} [3, 0]
{x < 0} or {x ≥ 2} (∞,0) ∪ [2,∞)
0 2
This last example has two separate regions on the number line that form the set.
In set notation we use the word "or" to indicate this, and in interval notation we use the notation
"∪" to indicate the Union of the two regions.
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2. Try these examples, and check your answers on the next page.
1. Write the set {8 < x ≤ 20} in interval notation.
2. Write the interval [4,∞) in set notation.
3. Write the domain and the range of the function shown below.
Use interval notation to describe both sets.
(4,3)
(5,2)
4. Determine the domain and the range of the quadratic function y = x2 + 7
5. Draw the graph of any relation that has the domain [2, ∞) and the range [0,4).
For more examples and notes on interval notation, see this YouTube video:
http://www.youtube.com/watch?v=hqg85P0ZMZ4
2
3. Answers:
1. (8,20]
2. x ≥ 4
3. Domain: [4,5) Range (2,3]
4. Domain (∞,∞) Range [7,∞)
5. Answers may vary, but here is one example:
(3,4)
(2,1)
(5,0)
3
![Interval Notation
Interval notation is a mathematical notation designed to describe a set of real
numbers. It is another way to write the domain or range of a relation.
In previous math courses, you have used set notation to describe a set of real
numbers.
Examples:
1. The set of real numbers greater than 2 is written in set notation as {x > 2}
and can be sketched on a number line as:
2 Note the open dot at 2.
This means that we don't include the
number 2 in the set.
2. The set { 5 ≤ x < 3} describes the set of real numbers between 5 and 3,
and includes the endpoint 5 in the set.
On a number line, this can be sketched as:
5 3
Note the closed dot at 5 and the open dot at 3
This means that we include the number 5 in the
set, but don't include the 3.
In interval notation, the set {x > 2} is written in the form (2,∞).
The round parenthesis indicates that we do not include the 2 in the set.
We always have a round parenthesis at ∞ or ∞.
The set { 5 ≤ x < 3} is written as [5,3) in interval notation.
The square parenthesis indicates that we include the endpoint 5 in the set.
Round parentheses correspond to open dots on sign diagrams, and square
parentheses correspond to the solid dots.
We use the notation (∞,∞) to indicate the set of all real numbers, or R.
Here are some more examples:
Set Notation Interval Notation
{ x ≤ 4} (∞,4]
{2 < x ≤ 6} (2,6]
{3 ≤ x ≤ 0} [3, 0]
{x < 0} or {x ≥ 2} (∞,0) ∪ [2,∞)
0 2
This last example has two separate regions on the number line that form the set.
In set notation we use the word "or" to indicate this, and in interval notation we use the notation
"∪" to indicate the Union of the two regions.
1](https://image.slidesharecdn.com/grade10intervalnotation-110215144418-phpapp02/85/Interval-Notation-1-320.jpg)
