Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 11: 71

Answer

(a): $Domain (f)= [4,8], Range (f)=[5,9]$ (b): $Domain (f)= [1,5], Range (f)=[2,6]$ (c): $Domain (f)= [4,8], Range (f)=[2,6]$ (d): $Domain (f)= [4,8], Range (f)=[6,18]$

Work Step by Step

The domain of any function consists of the values it can take on the x-axis, whereas the range consists of the values it can take on the y-axis. Here, we apply the given transformation to see how the domain and range have changed: (a): $Domain (f)= [4,8], Range (f)=[5,9]$ where the graph is shifted upward a distance of 3 units. (b): $Domain (f)= [1,5], Range (f)=[2,6]$ where the graph is shifted left a distance of 3 units. (c): $Domain (f)= [4,8], Range (f)=[2,6]$ where the graph is only compressed horizontally by the factor 3. (d): $Domain (f)= [4,8], Range (f)=[6,18]$ where the graph is stretched vertically by the factor 3.
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.