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: 48

Answer

Refer to the black graph below.
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Work Step by Step

Graph the parent function $ y=\sqrt{x}$. (refer to the attached image below) RECALL: The function $y=a\cdot f(x)$ involves either of the following transformations of the parent function $f(x)$: (i) a vertical stretch by a factor of $a$ if $a\gt0$, or (ii) a vertical compression if $0\lt a \lt 1$. The given function has $a=\frac{1}{2}$. This means that the graph of the given function involves a vertical compression of the parent function. Thus, to graph the given function, multiply each y-value of the parent function by $\frac{1}{2}$ while retaining the x-value of each point.. Refer to the attached image in the answer part above.
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