Interval NotationExpressing Inequalities in Interval Notation

Notation-

Inequalities < or > can be expressed using parentheses. On a number line, these symbols are noted with an OPEN point

Inequalities or can be expressed using brackets. On a number line, these symbols are noted with a SOLID point.

Picture Summary

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INEQUALITY NOTATION

INTERVAL NOTATION

Example

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INEQUALITY NOTATION

INTERVAL NOTATION

2 4x

[ 2,4)

Set Builder Notation

2 4x

| 2 4x x

This is read “x such that negative two is less than or equal to x is less than four.”

Example

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INTERVAL NOTATION

SET BUILDER NOTATION | 1 or 3x x x

( , 1) [3, )

Given Set Builder Notation…

| 6x x

Given Set Builder Notation…

| 2x x

Given Inequality Notation…

| 1 or 3x x x

Given Inequality Notation…

2 4x

Given Interval Notation…

( 3, 2]

Given Interval Notation…

( , 1] (4, )

Increasing

As the x-values increase, the y-values also increase.

Pictorially, this would appear to be a positive slope.

4

2

-2

-4

-6

-5 5

(5,2)

(4,4)

(2,-4)(0,-4)

(-2,4)

(-5,-2)

5, 2

2, 4

Decreasing

As the x-values increase, the y-values decrease.

Pictorially, this would appear to be a negative slope. 4

2

-2

-4

-6

-5 5

(5,2)

(4,4)

(2,-4)(0,-4)

(-2,4)

(-5,-2)

2, 0

4, 5

Constant

As the x-values increase, the y-values stay the same.

Pictorially, this would appear to be a zero slope.

4

2

-2

-4

-6

-5 5

(5,2)

(4,4)

(2,-4)(0,-4)

(-2,4)

(-5,-2)

0, 2

Positive

The x-values for which y-values are positive.

Pictorially, this would appear above the x-axis.

4

2

-2

-4

-6

-5 5

(5,2)

(4,4)

(2,-4)(0,-4)

(-2,4)

(-5,-2)

4, 1

(3, 5 ]

Negative

The x-values for which y-values are negative.

Pictorially, this would appear below the x-axis.

4

2

-2

-4

-6

-5 5

(5,2)

(4,4)

(2,-4)(0,-4)

(-2,4)

(-5,-2)

1, 3

Assignment

Before you leave – Check for Understanding due Assignment – “Introducing Interval Notation”