Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises - Page 298: 72

Answer

Refer to the blue graph below.
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Work Step by Step

RECALL: (1) The graph of the function $y=f(x) + k$ involves a vertical shift of $|k|$ units (upward when $k$ is positive, downward when $k$ is negative) of the parent function $y=f(x)$. (2) The graph of the function $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h$ is positive, to the left when $h$ is negative) of the parent function $y=f(x)$. (3) The graph of the function $y=-f(x)$ involves a reflection across the x-axis of the parent function $y=f(x)$. (4) The graph of the function $y=f(-x)$ involves a reflection across the y-axis of the parent function $y=f(x)$. (5) The graph of the function $y=a\cdot f(x)$ involves either a vertical stretch of the parent function $y=f(x)$ when $a \gt 1$ or a vertical shrink when $0 \lt a\lt 1$. (6) The graph of the function $y=f(ax)$ involves either a horizontal stretch of the parent function $y=f(x)$ when $0 \lt a \lt 1$ or a horizontal shrink when $a\gt 1$. The parent function of the given function is $y=\sqrt{x}$. Graph this function. (Refer to the black graph below.) The given equation is of the form $y=-f(x)+k$ with $k=-2$. Thus it involves the following graph transformations of the parent function $y=\sqrt{x}$: (1) a reflection across the x-axis (refer to the orange graph below); and (2) a 2-unit shift downward (refer to the blue graph in the answer part above.
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