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: 39


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

Work Step by Step

We see that the graph consists of the line $y=1$ from $-\infty$ to 0 and the horizontal line $y=2$ after. 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: $f(x)=\left\{\begin{array}{l} x~~~\ \mathrm{i}\mathrm{f}~~\ x\leq 0\\ 2~~~\ \mathrm{i}\mathrm{f}~~\ x\gt 0 \end{array}\right.$ We see that the domain is all real numbers, while the range consists of all negative numbers, including 0 and 2: Domain: $(-\infty,\ \infty)$ Range: $(-\infty,0$] $\cup\{2\}$
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