Interval Notation Worksheet - Weebly

Note to Teachers

This worksheet is simply meant to help students understand interval notation.

Teachers should feel free to add any problems or activities to this worksheet that

they may desire. Also the line graphs have been left blank and teachers need to

fill them in before copying for their class.

Interval Notation Worksheet

When describing a solution there are several methods to demonstrate the

answer. In the past we have used inequality notation, set builder notation, and

graphs (see below for examples); the purpose of this worksheet is to introduce

another method called interval notation.

Notation

graph

What does it look like?

How do you say it?

All numbers greater

than or equal to three

Set Notation

{ x x 3}

Inequality Notation

x 3

Interval Notation

[3, )

The set of all x ¡¯s such

that x is greater than

or equal to three

x is greater than or

equal to three

The interval from three

to infinity, inclusive of

three

Just like a filled in dot means that a point is included in the graph, or that it can

be ¡°equal to¡±, the bracket or ¡°[¡° means that a point is included or inclusive.

If a point is not included it would be shown graphically as an open dot, and in

interval notation is represented by parentheses ¡°(¡°.

Since it is not possible to reach infinity , the symbol next to it must always be

the parentheses. When going in the negative direction infinity is written - , or

negative infinity.

Fill in the missing spaces in the following table to practice these different

notations.

1.

Set Notation

{x | x < 4}

2.

{ x | 5 ¡Ü x ¡Ü 8}|

Graph

Interval Notation

[2,

3.

4.

{x | -3 < x < 14}

5.

{x | x ¡Ý -8}

[2,4) U (6,

6.

7.

{x | x < -2 or x ¡Ý 5}

8.

{x |-2 ¡Ü x < 0 or x > 1}

9.

(-

)

)

, 3] U [5,12]

10. How does the graph change if a ¡°less than¡± symbol is replaced by a ¡°less

than or equal to¡± symbol?

11. How would you say ¡°{ x -3 x 4}¡±? Make sure you write your answer as a

complete sentence.

12. Explain the difference between ¡°[¡°and ¡°(¡° in interval notation. How do you

determine which to use?

Graph the following function on a coordinate plane and then describe the domain

and range in interval notation. Use and label an appropriate scale.

13.

f ( x)

x 2 3x 1

Domain:

Range:

14.

g ( x)

x +2

Domain:

Range:

15.

h( x)

x 1 3

Domain:

Range:

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