Question 65116
graph
{{{F(x)=(x-2)/(x+4)}}}
Because the leading terms in the denominator and numerator have the same degree and coefficients, there is a horizontal asymptote of y=1/1=1.  I usually draw a faint dashed line for the asymptotes, because your graph can't equal that.
There is a vertical asymptote where the rational function is undefined (where the denominator=0).
The vertical asymptote is:
x+4=0
x+4-4=0-4
x=-4  Draw a faint dashed line there (unfortunatley this program is going to draw a solid dashed line there.)
Pick two numbers on both sides of the asymptote to plot.
If x=-8
{{{f(-8)=(-8-2)/(-8+4)}}}
{{{f(-8)=-10/(-4)}}}
{{{f(-8)=5/2}}} or 2.5
Plot (-8,5/2)
If x=-6
{{{f(-6)=(-6-2)/(-6+4)}}}
{{{f(-6)=-8/(-2)}}}
{{{f(-6)=4}}}
Plot (-6,4)
If x=-2
{{{f(-2)=(-2-2)/(-2+4)}}}
{{{f(-2)=-4/2}}}
{{{f(-2)=-2}}}
Plot (-2,-2)
If x=0
{{{f(0)=(0-2)/(0+4)}}}
{{{f(0)=-2/4}}}
{{{f(0)=-1/2}}}
Plot (0,-1/2)
This equation has an x-intercept when the numerator=0.
x-2=0
x-2+2=0+2
x=2  Plot (2,0)
After you connect the points remembering not to cross the asymptotes you get this:  Note this program draws in the vertical asymptote x=-4, it is not part of the graph.
{{{graph(300,200,-10,10,-10,10,(x-2)/(x+4))}}}
Happy Calculating!!!