Question

Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q18

Answer 1

`R(x)=(x+14)/(x(x+20))`

(a)

Since we can't divide by 0, we need to check the denominator in order to find the restrictions over the domain:

`\begin{gathered} x(x+20)=0 \\ so: \\ x=0 \\ or \\ x=-20 \end{gathered}`

Therefore, the domain is:

`\lbrace x|x\\e0_{\text{ }}and_{\text{ }}x\\e-20\rbrace`

Answer:

B

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(b)

The vertical asymptotes are located at the restriction points. So, the vertical asymptotes are:

`x=0,-20`

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(c)

Since:

`\lim_(x\rightarrow\pm\infty)f(x)=\lim_(x\rightarrow\pm\infty)(x+14)/(x(20+x))=0`

We can conclude that the horizontal asymptote is located at:

`y=0`

(d)

Answer:

A