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: 36

Answer

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

Work Step by Step

We see that the graph is a horizontal line $y=1$, except for a discontinuity at $x=0$, where the graph jumps to $(0,0)$. Thus we have: $f(x)=\left\{\begin{array}{l} 1\ ~~~\mathrm{i}\mathrm{f}~~\mathrm{x}\ \neq 0\\ 0\ ~~~\mathrm{i}\mathrm{f}~~\ x=0 \end{array}\right.$ The domain is all real numbers, while the range is either $0$ or $1$: Domain: $(-\infty,\infty)$ Range: $\{0$, 1 $\}$
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