Write a rational function that has a vertical asymptote of x=0, a horizontal asymptote of y=1/2

Mathematics

1 answer:

andreev551 [17]2 years ago

8 0

X
----
2x

check out the rules of HA!

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$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ x &,& y~) 
% (c,d)
&&(~ -9 &,& -1~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
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\begin{cases}
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\boxed{x=25}\\
-------\\
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\boxed{y=29}
\end{cases}$

$\bf -------------------------------\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ x &,& y~) 
% (c,d)
&&(~10 &,& 12~)
\end{array}\qquad
\\\\\\
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\begin{cases}
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\boxed{x=2}\\
-------\\
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\boxed{y=6}
\end{cases}$

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