Ive been stuck on this quest from textbook and I can't find an answer for it..
Question is, what may the equation of a rational function with below conditions look like? Explain how you got the equation.
$\displaystyle f(1)=0$
$\displaystyle \lim_{x \to 0} \; f(x)= - \infty$
$\displaystyle \lim_{x\to2^+} f(x)= -\infty$ (from right side)
$\displaystyle \lim_{ x \to 2^-} f(x)= +\infty$ (from left side)
$\displaystyle \lim_{x \to \pm \infty} f(x)= 0$