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

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.