Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 212: 48b



Work Step by Step

Since the graph follows the shape $f(x)=x^3$ we will start with that equation: $f(x)=x^3$ First notice the function is reflected across the y-axis. To reflect across the y-axis substitute -x for x in the right side of the equation: $f(x)=(-x)^3=-x^3$ Second, notice the graph has been stretched vertically (by a factor of k) and will follow the below equation: $f(x)=-kx^3$ Substitute (1,-2) into the above equation to solve for k: $-2=-k(1)^3$ $k=2$ So we get the final function: $f(x)=-2x^3$
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