Answer
Domain: $[-4,1)$
Range: $(-infinity, 2]$
Work Step by Step
$$Domain$$
The domain represents all the values of $x$ that the function $f(x)$ allows. In the exercise, the graph of $f(x)$ begins with point $(-4,0)$ and then continues. However, $f(x)$ is bound by a vertical asymptote which it cannot cross. Since there is no graph of $f(x)$ on the other side of the asymptote, we are forced to conclude that $f(x)$ is defined only until $x=1$ without including said value. Therefore, the Domain of $f(x)$ is {$x| -4\leq x\lt1$, where $x$ belongs to the realm of Real numbers}, also expressed as $[-4, 1)$ because it includes -4 but not 1.
$$Range$$
The Range, on the other hand, represents all the values of $f(x)$ that result from the function's domain. From the function's graph, we observe that it's highest value on the vertical axis is $2$ before descending unto negative infinity. Therefore, the range of the function can be expressed as $(-infinity, 2]$ since the value 2 is included in $f(x)$.