(Solved): 10. (10 pts) Consider the following rational functions: \[ r(x)=\frac{2 x-1}{x^{2}-x-2} \quad s(x)= ...

10. (10 pts) Consider the following rational functions: \[ r(x)=\frac{2 x-1}{x^{2}-x-2} \quad s(x)=\frac{x^{3}+27}{x^{2}+4} \quad t(x)=\frac{x^{3}-9 x}{x+2} \quad u(x)=\frac{x^{2}+x-6}{x^{2}-25} \quad w(x)=\frac{x^{3}+6 x^{2}+9 x}{x+3} \] (a) Which of these functions has a horizontal asymptote? (There may or may not be more than one.) Give the equation of the horizontal asymptote for each that does. (b) Which of these functions does not have a vertical asymptote? (There may or may not be more than one.) (c) One of these functions has a hole in its graph. Which one? Find the coordinates of the hole. (d) For \( u(x) \), find the \( y \)-intercept, \( x \)-intercept(s), and vertical asymptote(s).