Intermediate Algebra (11th edition)

In the interval the infinity symbol does not indicate a number—it

shows that the interval includes all real numbers greater than. The left parenthesis

indicates that is not included. A parenthesis is always used next to the infinity

symbol.

The set of all real numbers is written in interval notation as 1 ˆ, ˆ 2.

- 2

- 2

1 - 2, q 2 , ˆ

10 CHAPTER 1 Review of the Real Number System

NOW TRY
EXERCISE 9
Write in interval notation and
graph.

5 x |x6- 26

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

The interval (–∞, 4)

–8 –6 –4 –2 0 2

–6 is included.

The interval (–∞, – 6]

FIGURE 12

NOW TRY
EXERCISE 10
Write in interval notation and
graph.

5 x |xÚ 16

–6 –4 –2 0 2 4 6

The interval [– 4, ∞)

–4 –2 0 2 4 6

The interval (–2, 4)

FIGURE 14

NOW TRY

The set includes all real numbers less than or equal to To show

that is part of the set, a square bracket is used at as shown in FIGURE 12. In in-

terval notation, this set is written 1 - q, - 64.

- 6 - 6,

5 x |x...- 66 - 6.

Graphing an Inequality Written in Interval Notation

Write in interval notation and graph the interval.

This set is written in interval notation as The graph is shown in FIGURE 13.

We use a square bracket at -4,since - 4 is part of the set.

3 - 4, q 2.

5 x |xÚ- 46

EXAMPLE 10

NOW TRY

We sometimes graph sets of numbers that are betweentwo given numbers. For

example, the set

includes all real numbers between and 4, but notthe numbers and 4 them-

selves. This set is written in interval notation as The graph has a heavy line

between and 4, with parentheses at and 4. See FIGURE 14. The inequality

called a three-part inequality,is read “ is less than xand xis less

than 4,” or “xis between - 2 and 4.”

- 26 x 6 4, - 2

- 2 - 2

1 - 2, 42.

- 2 - 2

5 x |- 26 x 646

NOW TRY ANSWERS
9.

10. 3 1, q 2

1 - q, - 22

–1 0 1 2 3

–4 –3 –2 –1 0

FIGURE 11

FIGURE 13

Graphing an Inequality Written in Interval Notation

Write in interval notation and graph the interval.

The interval is written The graph is shown in FIGURE 11. Since the ele-

ments of the set are all real numbers less than4, the graph extends to the left.

1 - q, 4 2.

5 x |x 646

EXAMPLE 9