Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Appendix D - Graphing Techniques - Exercises - Page 447: 66

Answer

The graph shown should have undergone a combination of the transformations of $g(x) = \sqrt{x}$. The equation of the graph is $y=−\sqrt{x+4}+2.$

Work Step by Step

As there is no sign of any symmetry across neither the $x$-axis nor the $y$-axis, the graph shown should have undergone a combination of the transformations of $g(x) = \sqrt{x}$. Since reflection across the x-axis is noticed, a 'negative' sign should be multiplied, horizontal translation to the left by 4 units is found, x should be replaced by 'x+4' and vertical translation up by 2 units is shown, a value of '2' should be added. Hence, the equation of the graph is $y=−\sqrt{x+4}+2.$
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