University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 20


$\mathrm{Domain:}\ \ \ (-\infty ,0)\cup (0,\infty)$ $\mathrm{See\:the\:graph\:below.}$

Work Step by Step

$\mathrm{Remember:}$ The limiting factor on the domain for a rational function is the denominator, which cannot be equal to zero. Take the denominator of the rational function and compare it to zero to get the un-defined points. $|t|=0$ $t=0$ So the function is undefined at $\ t=0.\ $ Therefore, the function domain is $\ (-\infty,0)\cup (0,\infty).$ The graph of the given function $\ G(t)=\frac{1}{|t|}\ $ is similar to the graph of $\ y=\frac{1}{t}\ $, when $\ t\ $ is positive. When $\ t\ $ is negative, the graph of the given function will be the reflection of the graph of the function $\ y=\frac{1}{t}\ $ along the $\mathrm{y-axis}.$ See the graph below.
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