Question

Use graphs to find each set. $$(-4,0) \cup[-2,1]$$

   Use graphs to find each set.
$$(-4,0) \cup[-2,1]$$

Precalculus

Robert Blitzer 6th Edition

Chapter 0, Problem 18

Instant Answer

Solved by Expert Hannah Wilkinson

08/24/2021

Step 1

The parentheses "()" indicate that the number is not included in the set, while the brackets "[]" indicate that the number is included in the set. Show more…

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Use graphs to find each set. $$(-4,0) \cup[-2,1]$$

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Key Concepts

Open and Closed Intervals

The distinction between open and closed intervals is key in understanding interval notation. An open interval, denoted by parentheses, excludes its endpoints, meaning the smallest or largest value is not part of the set. A closed interval, denoted by brackets, includes its endpoints. This concept is important for determining exactly which numbers are part of a set, especially when combining intervals.

Graphical Representation on a Number Line

Graphing intervals on a number line provides a visual representation of the range of numbers included in the set. Each interval can be depicted by a segment on the line, with open or closed circles at the endpoints to indicate whether those points are included. This helps in understanding how different intervals overlap or combine.

Interval Notation

Interval notation is a concise way of describing subsets of the real numbers. It uses parentheses to denote that an endpoint is not included (open interval) and brackets to indicate that it is included (closed interval). This notation makes it easy to represent intervals and their combinations, which is essential for expressing solutions in calculus and algebra.

Union of Sets

The union of sets is the operation that combines all the elements of two or more sets, ensuring that each element is only represented once. In the context of interval notation, the union symbol '?' is used to combine intervals so that all points belonging to either interval are included in the final set.

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