University:
Montgomery College
Course:
MATH 050: Foundations of Algebra
Academic year:

2019
Views:

40

Pages:

2
Author:

Elaina Rivers

Section 4.1 Interval and Set-builder Notation Interval Notation We have already used set-builder notation to express an interval or intervals on the real number line. Another way to express intervals is by using interval notation. In interval notation, brackets indicate that the endpoints of the interval are included, and parentheses indicate that the endpoints are not included. The following chart shows how these are used. Graph Set-builder Notation Interval Notation Type of Interval [ a ] b { x a ≤ x ≤ b} [ a, b] Closed interval ( a ) b { x a < x < b} ( a, b) Open interval ( a ] b { x a < x ≤ b} (a,b] Half-open interval [ a ) b { x a ≤ x < b} [a,b) Half-open interval [ a { x x ≥ a} [ a, ∞ ) Infinite interval ( a { x x > a} ( a, ∞ ) Infinite interval ] b { x x ≤ b} (−∞, b] Infinite interval ) b { x x < b} (−∞, b) Infinite interval The notation (−∞, ∞) is used to represent the entire real number line, that is, all real numbers. 1. A portion of the real number system is represented in each problem using a graph, setbuilder notation, or interval notation. Re-express each interval in the two alternative representations. Graph Set-builder notation Interval Notation (a) { x −3 ≤ x ≤ 1} (b) ( 0 ) x 5 OVER Graph Set-builder notation Interval Notation (c) (-8, 2] (d) { x x > −4} (e) ] 2 x (f) (−3, ∞) (g) 2. { x x ≤ 1} Using Interval and Set-builder Notation to State Domain and Range Determine the domain and range of the following functions and state your answers in both interval and set-builder notation. (a) (b). Domain (interval notation): Domain (interval notation): Domain (set-builder notation): Domain (set-builder notation): Range (interval notation): Range (interval notation): Range (set-builder notation): Range (set-builder notation):