College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.2 - Graphs of Functions - 2.2 Exercises: 55

Answer

The curve is not a function of $x$.

Work Step by Step

RECALL: The Vertical Line Test states that if all vertical lines will pass through a graph in at most one point, then the graph represents a function of $x$. Note that the vertical line $x=-1$ passes through the given graph in an infinite number of points. The given graph fails the vertical line test. Thus, the graph does not represent a function of $x$. The domain is the set of $x$ values covered by the graph, while the range is the set of $y$ values covered by the graph of the function. The graph covers the x-values from $-3$ to $2$. Thus, the domain is $[-3, 2]$. The graph covers the y-values from $-2$ to $2$, Thus, the range is $[-2, 2]$.
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