Download Precalculus Name: Notes on Interval Notation I. Bounded Intervals

Precalculus
Notes on Interval Notation
Name: _________________________________
I. Bounded Intervals on the Real Number Line
Interval Type
Interval Notation Set-Builder Notation
Closed
Graph
Open
Half-Open
Unbounded Interval
All Real Numbers
*** Remember that infinity is NOT a number. The symbols used represent the unboundedness of an interval.
II. Examples
A. Write an inequality to represent each of the intervals and state if it is bounded or unbounded.
1. (−3, 5]
2. (−4, ∞)
3. [0, 2]
B. Use interval notation to describe the subset or real numbers represented by the inequality. Graph
1. −7 ≤ 𝑥 < −3
2. 𝑥 ≥ 12
3. 𝑥 < 5
C. Use inequality and interval notation to describe each of the following.
1. c is nonnegative
2. b is at most 6
4. d is negative and greater than -3
3. a is at least 12
5. x is positive or x is less than -6
Homework! Pg 7 #14 – 30 even, Pg 91 #4 – 10 even, 20 – 30 even
Precalculus
Notes on Interval Notation
10/18/12
I. Bounded Intervals on the Real Number Line
Interval Type
Interval Notation Set-Builder Notation
Closed
[a, b]
{𝑥|𝑎 ≤ 𝑥 ≤ 𝑏}
Open
(a, b)
{𝑥|𝑎 < 𝑥 < 𝑏}
Half-Open
[a, b)
{𝑥|𝑎 ≤ 𝑥 < 𝑏}
(a, b]
{𝑥|𝑎 < 𝑥 ≤ 𝑏}
Unbounded Interval
[𝑎, ∞)
{𝑥|𝑥 ≥ 𝑎}
(𝑎, ∞)
{𝑥|𝑥 > 𝑎}
(−∞, 𝑎]
{𝑥|𝑥 ≤ 𝑎}
(−∞, 𝑎)
{𝑥|𝑥 < 𝑎}
All Real Numbers
(−∞, ∞)
{𝑥|𝑥 𝑖𝑠 𝑟𝑒𝑎𝑙}
Graph
*** Remember that infinity is NOT a number. The symbols used represent the unboundedness of an interval.
II. Examples
A. Write an inequality to represent each of the intervals and state if it is bounded or unbounded.
1. (−3, 5]
−𝟑<𝒙≤𝟓
Bounded
2. (−4, ∞)
−𝟒<𝒙<∞
Unbounded
3. [0, 2]
𝟎≤𝒙≤𝟐
Bounded
B. Use interval notation to describe the subset or real numbers represented by the inequality. Graph
1. −7 ≤ 𝑥 < −3
[−𝟕, 𝟑)
2. 𝑥 ≥ 12
𝟏𝟐 ≤ 𝒙 < ∞
3. 𝑥 < 5
−∞<𝒙<𝟓
C. Use inequality and interval notation to describe each of the following.
1. c is nonnegative
𝒄 ≥ 𝟎 [𝟎, ∞)
2. b is at most 6
𝒃≤𝟔
(−∞, 𝟔]
4. d is negative and greater than -3
𝒅 < 𝟎 𝒂𝒏𝒅 𝒅 > −𝟑 𝒔𝒐 … − 𝟑 < 𝒅 < 𝟎
(−𝟑, 𝟎)
3. a is at least 12
𝒂 ≥ 𝟏𝟐
[𝟏𝟐, ∞)
5. x is positive or x is less than -6
𝒙 > 𝟎 𝒐𝒓 𝒙 < −𝟔
(−∞, −𝟔) ∪ (𝟎, ∞)
Homework! Pg 7 #14 – 30 even, Pg 91 #4 – 10 even, 20 – 30 even