Consider the rational function .

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Consider the rational function

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

. (i) State the domain of

g

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

g

on its domain. (iii) Find the intervals where

g

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

y=g(x)

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