Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 4 - An Introduction to Functions - 4-4 Graphing a Function Rule - Practice and Problem-Solving Exercises - Page 258: 31

Answer

The graph of $y=x^3$ is graphed below and to graph the function $y=−x^3$ we need to vertically reflect the graph of $y=x^3$ (reflection over the x-axis). To graph $y=−x^3$ we multiply each y-value by -1 while keeping the x value the same. So for example, the point (1,1) of function $y=x^3$ becomes (1,-1) for the function $y=−x^3$.
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Work Step by Step

The graph of $y=x^3$ is graphed below and to graph the function $y=−x^3$ we need to vertically reflect the graph of $y=x^3$ (reflection over the x-axis). To graph $y=−x^3$ we multiply each y-value by -1 while keeping the x value the same. So for example, the point (1,1) of function $y=x^3$ becomes (1,-1) for the function $y=−x^3$.
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