Question

Write a rational function whose vertical asymptotes are at x = 1, x = 3, x = -5 and whose horizontal

asymptote is at y = -4. Sketch the function on the coordinate plane and show its table of values.

Answer 1

$$y=-4\dfrac{x^3}{(x+5)(x-1)(x-3)}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} x & y \\ \hline \\ -30 & -\dfrac{1440}{341} \\ \\ -7 & -\dfrac{343}{40} \\ \\ -6 & -\dfrac{96}{7} \\ \\ -4 & \dfrac{256}{35} \\ \\ -3 & \dfrac{9}{4} \\ \\ 0 & 0 \\ \\ -\dfrac{1}{2} & \dfrac{4}{189} \\ \\ \dfrac{1}{2} & -\dfrac{4}{55} \\ \\ \dfrac{3}{2} & -\dfrac{36}{13} \\ \\ 2 & \dfrac{32}{7} \\ \\ 4 & -\dfrac{256}{27} \\ \\ 5 & -\dfrac{25}{4} \\ \\ 30 & -\dfrac{800}{203} \\ \\ \end{array}$$