Characteristics of Rational Functions
Determine the Horizontal Asymptote for each of the following functions. If it doesn't exist, write DNE.

Rational FunctionHorizontal Asymptote
f(x)=5x410x21\displaystyle {f{{\left({x}\right)}}}=\frac{{-{5}{x}-{4}}}{{-{10}{x}^{{2}}-{1}}}
g(x)=28x77x2\displaystyle {g{{\left({x}\right)}}}=\frac{{{28}{x}-{7}}}{{{7}{x}-{2}}}
p(t)=t24t+8\displaystyle {p}{\left({t}\right)}=\frac{{t}^{{2}}}{{{4}{t}+{8}}}
f(x)=992x2\displaystyle {f{{\left({x}\right)}}}=\frac{{-{9}}}{{{9}-{2}{x}^{{2}}}}