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