Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Section 2.2 - Graphs of Functions - 2.2 Exercises - Page 168: 56

Answer

The graph represents a function. Domain: $[-3, 2]$ Range: $[-2, -2] \cup (0, 3]$

Work Step by Step

All vertical lines will pass through at most one point on the graph. (Note that at x=-1, the line will pass through (-1, -2), a solid dot, but not through (-1, 0), a hole or hollow dot). Thus, the graph pass the vertical line test which means that it represents a function. The x-values vary from -3 to 2 so the domain is $[-3, 2]$. The y-values range from 0 to 3 (but not including 0), and also includes -2. Thus, the range is $(-1, 2] \cup [-2,-2]$
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