Mathematics

Problem

Consider the rational function

g(x)=\dfrac{2x}{x-1}

. a. (i) State the domain of

g

and write the equations of all vertical and horizontal asymptotes. b. (ii) Find the critical point(s) of

g

on its domain. c. (iii) Find the intervals where

g

is strictly increasing and where it is strictly decreasing. d. (iv) Sketch a neat graph of

y=g(x)

, marking clearly the intercepts, asymptotes and the nature of the turning point.