University Calculus: Early Transcendentals (3rd Edition)

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