College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.7 - Graphing Techniques - 2.7 Exercises - Page 256: 72


See the picture below.

Work Step by Step

By calculating the values of $f(x)=\frac{1}{2}x^3+2$ (with blue) and $g(x)=x^3$ (with red) we can see that the following equation is true: $\frac{1}{2}g(x)+2=f(x)$ In order to graph the parent function , here is the table of values: $g(-2)=-2^3=-8$ $g(-1)=-1^3=-1$ $g(0)=0^3=0$ $g(1)=1^3=1$ $g(2)=2^3=8$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^3$ but is wider (is shrinked vertically by a factor of 2) and is translated 2 units up.
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