University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 11: 7


(a) In Figure 1 the graph is not a function of x. (b) In Figure 2 the graph is a function of x

Work Step by Step

(a) The graph is not a function of x because there are vertical lines that intersect the curve twice. And we know that in order for it to be a function, each x must have a unique output, but in this case where the vertical line intersects twice, it indicates that the x value has two different y value outputs. (b) Using the above information from part a, there is no vertical lines intersecting the graph more than once, hence each x value only has one y value output. Therefore this is a function.
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