Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.1 - Radical Expressions and Graphs - 7.1 Exercises - Page 440: 51

Answer

Graph of $ f(x)=\sqrt[3]{x-3} $

Work Step by Step

Substituting values of $x$ in the given function, $ f(x)=\sqrt[3]{x-3} $, results to \begin{array}{l|c|r} \text{If }x=-5: & \text{If }x=2 & \text{If }x=3 \\\\ f(x)=y=\sqrt[3]{x-3} & f(x)=y=\sqrt[3]{x-3} & f(x)=y=\sqrt[3]{x-3} \\ y=\sqrt[3]{-5-3} & y=\sqrt[3]{2-3} & y=\sqrt[3]{3-3} \\ y=\sqrt[3]{-8} & y=\sqrt[3]{-1} & y=\sqrt[3]{0} \\ y=-2 & y=-1 & y=0 \end{array} \begin{array}{l|r} \text{If }x=4: & \text{If }x=11 \\\\ f(x)=y=\sqrt[3]{x-3} & f(x)=y=\sqrt[3]{x-3} \\ y=\sqrt[3]{4-3} & y=\sqrt[3]{11-3} \\ y=\sqrt[3]{1} & y=\sqrt[3]{8} \\ y=1 & y=2 .\end{array} Connecting the points $ \left(-5,-2\right), \left(2,-1\right), \left(3,0\right), \left(4,1\right), \text{ and } \left(11,2\right) $ with a curve gives the graph of $ f(x)=\sqrt[3]{x-3} $.
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