Question 854750
Vertical Asymptotes : When the denominator equals zero,
{{{x^2-4=0}}}
{{{(x-2)(x+2)=0}}}
{{{x=2}}}
and
{{{x=-2}}}
Horizontal asymptotes:
{{{lim(x-> infinity, (3+4/x^2)/(1-4/x^2))=3/1=3}}}
{{{y=3}}}
X-intercept: x when r(x)=0
{{{3x^2+4=0}}}
There is no x-intercept.
Y-intercept: y when x=0.
{{{r(0)=(3(0)+4)/(0^2-4)}}}
{{{r(0)=4/(-4)=-1}}}
.
.
.
{{{drawing(300,300,-10,10,-10,10,green(line(2,-10,2,10)),circle(0,-1,0.3),
green(line(-2,-10,-2,10)),grid(1),
green(line(-10,3,10,3)),
graph(300,300,-10,10,-10,10,(3x^2+4)/(x^2-4)))}}}