#### Answer

The Domain is $t \ne -1 $
the Range is: $(-\infty, -2) and (-2, \infty)$
The sketch is:

#### Work Step by Step

$g(t) = \frac{t^2 - 1}{t + 1}$
Lets find the Domain of the function
$t+1\ne0$
$t \ne -1 $
The Domain is $t \ne -1 $
Lets find the Range:
$g(t) = \frac{t^2 - 1}{t + 1} = \frac{(t-1)(t+1)}{t + 1}$
when $t \ne -1 $, $g(t) =(t-1)$
So the Range is: $(-\infty, -2) and (-2, \infty)$
The sketch is: