Characteristics of Rational Functions
Determine the Horizontal Asymptote for each of the following functions. If it doesn't exist, write DNE.
Rational Function
Horizontal Asymptote
f
(
x
)
=
−
5
x
−
4
−
10
x
2
−
1
\displaystyle {f{{\left({x}\right)}}}=\frac{{-{5}{x}-{4}}}{{-{10}{x}^{{2}}-{1}}}
f
(
x
)
=
−
10
x
2
−
1
−
5
x
−
4
g
(
x
)
=
28
x
−
7
7
x
−
2
\displaystyle {g{{\left({x}\right)}}}=\frac{{{28}{x}-{7}}}{{{7}{x}-{2}}}
g
(
x
)
=
7
x
−
2
28
x
−
7
p
(
t
)
=
t
2
4
t
+
8
\displaystyle {p}{\left({t}\right)}=\frac{{t}^{{2}}}{{{4}{t}+{8}}}
p
(
t
)
=
4
t
+
8
t
2
f
(
x
)
=
−
9
9
−
2
x
2
\displaystyle {f{{\left({x}\right)}}}=\frac{{-{9}}}{{{9}-{2}{x}^{{2}}}}
f
(
x
)
=
9
−
2
x
2
−
9
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