Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-5 Graphing Square Root Functions - Practice and Problem-Solving Exercises - Page 630: 53


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Work Step by Step

a. No. The graph fails the vertical line test as the x-values have multiple y-values. b. For $x=y^{2}$, it is easy to plug in y-values and graph the points. This is how we come across the x-values having multiple y-values. $y=\sqrt x$ is taken from $x=y^{2}$ by square rooting both sides. It has the positive range values for $x=y^{2}$ c. $y=$$-\sqrt x$; $y=\sqrt x$ gives us the positive range values for $x=y^{2}$, but we need to account for the negative range values. We cannot put a negative sign inside a radical, or else the outputs will be imaginary, so it goes outside the radical. This gives us the opposite values of $y=\sqrt x$.
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