Answer
1. Domain: $(-\infty ,3)\cup (3,\infty )$
2. Range: $(-\infty ,0)\cup (0,\infty )$
Work Step by Step
1. Remember, a rational function is only defined when its denominator part is not zero. We take the denominator of the function and compare it to zero to get the undefined points.
$3-t=0$
$\Rightarrow t=3$
So, the function is undefined at $ t=3$. So it will be excluded from the domain as it yields zero in the denominator.
Domain: $(-\infty ,3)\cup (3,\infty )$
2. Since $y=\frac{4}{3-t}$, $y$ can obtain any value except zero, because $y$ is a fraction with any value in the denominator (except zero).
Range: $(-\infty ,0)\cup (0,\infty )$
