Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 45



Work Step by Step

Since the shape of the graph is a $f(x) = \sqrt x$ we will start with that function: $f(x)=\sqrt x$ The first transformation is 6 units left. Remember that shifts to the left or right are done inside of the function and that left or right transformations have an opposite sign so that left shifts are positive and right shifts are negative. $f(x)=\sqrt{x+6}$ The reflection across the x-axis means multiply the right side by -1 $f(x)=-\sqrt{x+6}$ The reflection across the y-axis means change the sign of the x on the right side. $f(x)=-\sqrt{6-x}$
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