Question

Please help with the problem.

Answer 1

we have the rational function

`C(n)=(500)/(n)+81`

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

`\begin{gathered} C(n)=(500)/(n)+81 \\ C(n)=(500+81n)/(n) \end{gathered}`

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