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: 19


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

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 $\ (-\infty \:,\:0)\cup (0,\:\infty \:).$ When $\ t<0\ $, the value of the function $\ F(t)=\frac{t}{|t|}$ will be $\frac{-t}{t}=-1$. When $\ t>0\ $, the value of the function $\ F(t)=\frac{t}{|t|}$ will be $\frac{t}{t}=1$. So, we will have a horizontal line $\ y=-1\ $ when $\ t<0\ $ and $\ y=1\ $ when $\ t>0.\ $ See the graph below.
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