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: 42

Answer

$f(x)=\left\{\begin{array}{l} 3~~~~~~~~~~~~\ \mathrm{i}\mathrm{f}~~\ x=2\\ 2x-3~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \neq 2 \end{array}\right.$ Domain: $(-\infty,\ \infty)$ Range: $(-\infty,1)\cup(1,\ \infty)$

Work Step by Step

We see that the graph consists of the line $y=2x-3$, except that there is a jump discontinuity at $x=2$, where the $y$ value becomes $3$. Thus we have: $f(x)=\left\{\begin{array}{l} 3~~~~~~~~~~~~\ \mathrm{i}\mathrm{f}~~\ x=2\\ 2x-3~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \neq 2 \end{array}\right.$ We see that the domain is all real numbers, and the range is also all real numbers, excluding 1: Domain: $(-\infty,\ \infty)$ Range: $(-\infty,1)\cup(1,\ \infty)$
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