A function \(f\) has a horizontal asymptote of \(y = -4,\) a vertical asymptote of \(x = 3,\) and an \(x\)-intercept at \((1,0). \)
Part (a): Let \(f\) be of the form \(f(x) = \frac{ax+b}{x+c}.\) Find an expression for \(f(x).\)
Part (b): Let \(f\) be of the form \(f(x) = \frac{rx+s}{2x+t}.\) Find an expression for \(f(x).\)
