## 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 $\ (-\infty \:,\:0)\cup (0,\:\infty \:).$ 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.