Solve the below:
1. When preparing to graph the rational function y(x), this algebra is done.
(a) Specify, with reasons, the (largest) domain of y(x). (You needn't repeat algebra)
(b) Find where the graph crosses the y-axis.
y(x) = x^4 - 2x^3 - 3x^2 - 3x â?" 1
x^3 - 3x^2 + x - 3
= x + 1 -(x - 1)(x + 2)
(x - 3)(x^2 + 1)
= x + 1 -1/x -3 - 1/x^2 + 1
(c) Give all vertical asymptotes, and the graph's behaviour near such asymptotes.
(d) Specify the equation of the oblique asymptote to the graph, and the co-ordinates of all points, if any, where the graph crosses this asymptote.
(e) Specify the intervals of the x-axis, corresponding to values of y(x) which are greater than the corresponding point on the oblique asymptote.