Consider the following. x4 - x - 6 f(x) = - x3 - 4x2 - 11x + 30 (a) State the domain of the function. all real numbers x except x = 3, x = -2, and x = -5 all real numbers x except x = -5 all real numbers x except x = -3, x = 2, and x = 5 O all real numbers x O all real numbers x except x = 5 (b) Identify all intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) = (c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equations. If there are no asymptotes, enter DNE.)(d) Plot additional solution points as needed to sketch the graph of the rational function. 3' 15 15 15