Question 1067304
{{{f(x) = (2x-3x^2)/(2x^2-x-3)}}}={{{(-3x^2+2x)/(2(x^2-0.5x-1.5))}}}={{{(-3x^2+1.5x+4.5)/(2(x^2-0.5x-1.5))}}}+{{{(0.
5x-4.5)/(2(x^2-0.5x-1.5))}}}={{{-3/2}}}+{{{(0.
5x-4.5)/(2(x^2-0.5x-1.5))}}}
So, {{{lim(x->infinity,f(x))=-3/2}}} .
The horizontal asymptote is {{{highlight(y=-3/2)
}}} .
{{{graph(300,300,-5,5,-5,5,-3/2,(2x-3x^2)/(2x^2-x-3))}}}