we have the rational function
[tex]C(n)=\frac{500}{n}+81[/tex]Remember that, the denominator cannot be equal to zero
so
The domain of the given function is all real numbers, except for n=0
that means
For n=0 ----> there is a vertical asymptote
therefore
The vertical asymptote is n=0 (the y-axis)
using a graphing tool
see the attached figure below
Find out horizontal asymptote
we have
[tex]\begin{gathered} C(n)=\frac{500}{n}+81 \\ C(n)=\frac{500+81n}{n} \end{gathered}[/tex]Degree on Top is Equal to the Bottom
In this case, the graph has a horizontal asymptote along
C=81/1=81
the horizontal asymptote is at C=81
see the figure below
