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

Answer

(a) Not function of $x$ (b) 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 an 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) 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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