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

Answer

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

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.
Small 1532102633
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.