For every rational function below: (i) state domain, (ii) find all x- and y- intercepts, (iii) find any horizontal, vertical and slant asymptotes, (iv) using the facts (and plotting the few additional points) provide the rough sketch of function, but clearly showing asymptote lines.
a) f(x)= 5/(x-2)
b) g(x)= (x^2-2x-8)/(x^2-9)
c) h(x)= (x+2)/(x+4)
d) f(x)= (x^2+5)/x