Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 9: 11


B is a function; A isn't

Work Step by Step

Let's look at the function A first( in black). We immediately see that there is x axis symmetry and that we can draw a vertical line at any line $x=c$ where c is an arbitrary natural number. Thus it fails the vertical line test and isn't a function! Next we look at B which is pink. From what we see, it looks like simple harmonic motion or a sinusoidal curve. This kind of graph is a function since we cannot draw a vertical line ANYWHERE through 2 or more points. Thus it is a function.
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