Stitz-Zeager_College_Algebra_e-book

# Example 142 use the vertical line test to determine

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Unformatted text preview: etric about the x-axis (e.g. (1, −4) is on the graph but (1, 4) is not) The graph is not symmetric about the y -axis (e.g. (1, −4) is on the graph but (−1, −4) is not) The graph is symmetric about the origin 34 Relations and Functions 1.4 Introduction to Functions One of the core concepts in College Algebra is the function. There are many ways to describe a function and we begin by deﬁning a function as a special kind of relation. Definition 1.4. A relation in which each x-coordinate is matched with only one y -coordinate is said to describe y as a function of x. Example 1.4.1. Which of the following relations describe y as a function of x? 1. R1 = {(−2, 1), (1, 3), (1, 4), (3, −1)} 2. R2 = {(−2, 1), (1, 3), (2, 3), (3, −1)} Solution. A quick scan of the points in R1 reveals that the x-coordinate 1 is matched with two diﬀerent y -coordinates: namely 3 and 4. Hence in R1 , y is not a function of x. On the other hand, every x-coordinate in R2 occurs only once which means each x-coordinate has only one corresponding y -coordinate. So, R2 does represent y as a function of x. Note that...
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