College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding - Page 258: 45


Refer to the red graph in the attached image below for the graph.

Work Step by Step

Graph the parent function $ y=x^3$. (refer to green graph in the the attached image below) RECALL: (1) The function $y=f(x-h)$ involves a horizontal shift of either $h$ units to the right of the parent function $f(x)$ if $h \gt 0$, or $|h|$ units to the left when $h \lt0$ (2) The function $y=f(x)+k$ involves a vertical shift of either $k$ units upward of the parent function when $k\gt0$, or $|k|$ units downward when $k\lt0$. The given function involves both transformations mentioned in (1) and (2) above with $h=1$ and $k=2$ Thus, to graph the given function, perform the following: (i) Shift each plotted point of the parent function $y=\sqrt{x}$ one unit to the right (refer to the black graph in the attached image below); and (ii) Shift the resulting graph in (i) 2 units upward. (refer to the red graph in the attached image in the answer part above).
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