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Please help with the problem.

Sagot :

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

View image MabryV522026
View image MabryV522026
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