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: 3

Answer

The vertical line test is used to see if a graph represents a function.

Work Step by Step

The vertical line test is used to see if a graph represents a function. A vertical line is drawn through the graph at every point (every $x$ value), and if it intersects the graph in only one point, each time, then the graph represents a function. If the vertical line intersects the graph in more than one point, then the graph is not a function. In such a case there would exist two different $y$ values for the same $x$ value. For instance f(2)=5 and f(2)=10. Such a graph could not be a function because the dependent variable $y$ would have two "answers" or values for the same $x$ value. Functions must only have one $y$ value for a given $x$ value in order to make sense. For instance, if the function was modeling earnings ($y$) based on the amount of hours worked ($x$), there should only be one value for earnings if the person worked, say, 10 hours.
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