Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises: 61

Answer

The graph is a number line with a shaded region between -2 and 1 with open circles at -2 and 1.
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Work Step by Step

In interval notation parenthesis are non-inclusive are are represented using open circles. 1. Set (-2, 0) is all the numbers between -2 and 0 not including -2 or 0. 2. Set (-1, 1) is all the numbers between -1 and 1 not including -1 or 1. 3. The union (-2,0) U (-1, 1) is the combination of all numbers in either set. 4. This means that -1 is in the union because it is in the set (-2, 0). 5. And 0 is in the union because it is in the set (-1, 0). 6. Therefore, the union is the interval (-2, 1). 7. The graph is a number line with a shaded region between -2 and 1, and open circles at -2 and 1.
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