Question

f(x)=1+7/x-4/x^2

Find the vertical and horizontal asymptote(s)

Answer 1

\[f(x)=1+\frac{ 7 }{ x }-\frac{ 4 }{ x^2 }\]

Answer 2

Convert the sum of fractions to one big fraction by finding the common denom.
To find the horizontal asympt. compare the highest degree of the top and bottom. (if the these are equal then compare the coefficient for the terms with the highest degree)
Then factor the top and bottom to find the zeros of the top and bottom. Any zero in the bottom that can't be factored by the top tells you where a vertical asymptote is. Any zero that is factorable by the top tells you where a hole/discontinuity in the graph is.