MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions
Problem
Consider the function f(x)=x−12x+1 .
(1) Find the vertical asymptote of the function.
(2) Find the axes intercepts.
(3) Rearrange the function to find the horizontal asymptote.
(4) Draw a sign diagram of the function.
(5) Hence discuss the behaviour of the function near the asymptotes.
(6) Sketch the function, showing the features you have found.