Please present thorough work explaining step-by-step how to get the correct answer and please include units:

4. Suppose q is the rational function defined by q(x) = 5 + 19x -4 x2 + 7r + 12 (a) Determine the domain of q(r) and write the answer in interval notation. (b) Find the vertical asymptote(s), if any, of the graph of q(x). (Please make sure to justify your answer.) (c) Find the horizontal asymptote(s), if any, of the graph of q(x). (Please make sure to justify your answer.) (d) Find the coordinates of any hole(s) of the graph of q(x). (Please make sure to justify your answer.) (e) Determine the y-intercept of the graph of q(x)