College Algebra (11th Edition)

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

Chapter 2 - Section 2.6 - Graphs of Basic Functions - 2.6 Exercises - Page 240: 37

Answer

$f(x)=\left\{\begin{array}{l} 2~~~~~~\ \mathrm{i}\mathrm{f}~\ x\leq 0\\ -1~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \gt 1 \end{array}\right.$ Domain: $(-\infty,\ 0]\ \cup(1,\ \infty)$ Range: $\{-1,2\}$

Work Step by Step

We see that the graph consists of two horizontal lines, $y=2$ and $y=-1$. Solid circles indicate that the value belongs to that piece of the function (e.g. "$\leq$" or "$\geq$"), while open circles indicate that the value does not (e.g. "$\lt$" or "$\gt$"). Thus we have: $f(x)=\left\{\begin{array}{l} 2~~~~~~\ \mathrm{i}\mathrm{f}~\ x\leq 0\\ -1~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \gt 1 \end{array}\right.$ We see that the domain is all real numbers, except for the region between 0 and 1 (0 is included, while 1 is excluded). The range is either -1 or 2: Domain: $(-\infty,\ 0]\ \cup(1,\ \infty)$ Range: $\{-1,2\}$
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.