Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.1 Exercises - Page 876: 2


$z$ is a function of $x$ and $y$.

Work Step by Step

To determine if $z$ is the function of $x$ and $y$ we will use the parallel line test. If there is a line parallel to $z$ axis that intercepts the graph at two points, only then $z$ is not a function of $(x,y)$ because we would have two values of $z$ for the same ordered pair $(x,y)$, contrary to the definition of a function. On this graph we see that there is no such line so $z$ IS a function of $x$ and $y$.
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