Question 857340
X-intercepts : value of {{{x}}} when {{{f(x)=0}}}.
{{{f(x)=0}}} when the numerator equals zero.
{{{2x+1=0}}}
{{{2x=-1}}}
{{{x=-1/2}}}
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Vertical asymptotes : value of x when the denominator goes to zero.
{{{x-2=0}}}
{{{x=2}}}
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Horizontal asymptote : Divide numerator and denominator by largest leading term (in this case, {{{x}}}) and take the limit as x goes to infinity.
{{{y=lim(x->infinity,(2+1/x)/(1-2/x))=(2+0)/(1-0)=2/1=2}}}
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{{{drawing(300,300,-10,10,-10,10,grid(1),green(line(2,10,2,-10)),green(line(-10,2,10,2)),graph(300,300,-10,10,-10,10,(2x+1)/(x-2)))}}}