College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 243: 42

Answer

Refer to the blue graph below.
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Work Step by Step

RECALL: (1) The function $y=-f(x)$ involves a reflection about the x-axis of the parent function $f(x)$. (2) The function $y=a\cdot f(x)$ involves a vertical stretch of the parent function $f(x)$ when $a \gt 1$. The function will involve a vertical compression when $0 \lt a \lt 1$. The parent function of the given function is $y=\sqrt{x}$. The graph of the given function involves (1) a reflection about the x-axis, and (2) vertical stretch of the parent function $y=\sqrt{x}$. Thus, to graph the given function: (1) Graph the parent function $y=\sqrt{x}$ . (Refer to the red graph in the attached image below) (2) Reflect the parent function $y=\sqrt{x}$ about the x-axis by changing the y-coordinate of each point of the parent function to its opposite sign while retaining the x-coordinate. (refer to the orange graph in the attached image below) (3) Multiply $5$ to each y-value of function in Step (2)above while keeping the value of the x-coordinate of each point. (Refer to the blue graph in the attached image above.)
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