How does changing the value of $\dfrac{p}{q}$ affect the drawing of the graph (domain/range/shape, etc.) How do you calculate asymptotes?

Below is a question dealing with this type of function. Can someone please refer to the explanations on how to go about solving these questions? I have no idea because I don't understand these graphs

HINT :
The graph of $y=\sqrt[m]{(x-a)^n}$ is a graph such that the graph of $y=\sqrt[m]{x^n}$ is parallel-shifted by $a$ in the $x$ direction.
Since $y=f(x)$ has a maximal domain of $[-a, \infty)$...