Precalculus (6th Edition)

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

Chapter 2 - Graphs and Functions - 2.7 Graphing Techniques - 2.7 Exercises: 8

Answer

RECALL: (1) 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 $y=f(x)$. (2) 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 $y=f(x)$. The parent function of the given function is $y=x^3$. The given function can be written as $fx)=(x-3)^3+6$. Thus, the given function involves a horizontal and a vertical translation of the parent function $y=x^3$. Therefore, the missing expressions in the given statement (in order) are: $3$; $6$

Work Step by Step

RECALL: (1) 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 $y=f(x)$. (2) 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 $y=f(x)$. The parent function of the given function is $y=x^3$. The given function can be written as $fx)=(x-3)^3+6$. Thus, the given function involves a horizontal and a vertical translation of the parent function $y=x^3$. Since $h=3$ and $k=6$, then the graph of the given function involves a 3-unit shift to the right and 6-unit shift upward of the parent function $y=x^3$. Therefore, the missing expressions in the given statement (in order) are: $3$; $6$
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