We want to graph the rational function () =x3+4x2+x63x32x23x+2=q(x)p(x)

(a) Determine if the graph has -axis symmetry and/or -axis symmetry. Clearly explain your answer.

(b) Find the -intercept (if it exists).

(c) Find the possible -intercepts (if they exist) by finding the roots of () = 0.

(d) Find any vertical asymptote(s) by finding the roots of () = 0.

(e) What is the domain of ()?

(f) Are there any points on the graph that are holes?

(g) Find the horizontal asymptote (if it exists). Clearly explain your answer. 10

(h) Plot a few additional points between and beyond each -intercept and vertical asymptote. Graph ().

(i) Find the coordinates of any points where the graph crosses the horizontal asymptote. Are there any points where the graph crosses the vertical asymptotes?