Question 369255
{{{y=(1+2x)/(x+2)}}}  Vertical asymptote is when the denominator equals 0.  so x+2=0
x=-2

Horizontal asymptote in this problem would be the leading coefficients of the x values or {{{2/1}}} so the Horizontal asymptote is at y=2.  
You are right about the y-intercept at 1/2.  The x-intercept is where y=0 so set the equation equal to 0 and solve for x.

{{{y=(1+2x)/(x+2)=0}}}
{{{1+2x=0}}}
{{{x=-1/2}}}
The graph below shows the intercepts well:

{{{graph(300,200,-5,5,-1,5,(1+2x)/(x+2))}}}

The graph below shows the asymptotes well:
{{{graph(300,200,-10,10,-10,10,(1+2x)/(x+2))}}}