[tex]R(x)=\frac{x+14}{x(x+20)}[/tex]
(a)
Since we can't divide by 0, we need to check the denominator in order to find the restrictions over the domain:
[tex]\begin{gathered} x(x+20)=0 \\ so: \\ x=0 \\ or \\ x=-20 \end{gathered}[/tex]
Therefore, the domain is:
[tex]\lbrace x|x\ne0_{\text{ }}and_{\text{ }}x\ne-20\rbrace[/tex]
Answer:
B
------------------------------
(b)
The vertical asymptotes are located at the restriction points. So, the vertical asymptotes are:
[tex]x=0,-20[/tex]
----------------------
(c)
Since:
[tex]\lim_{x\rightarrow\pm\infty}f(x)=\lim_{x\rightarrow\pm\infty}\frac{x+14}{x(20+x)}=0[/tex]
We can conclude that the horizontal asymptote is located at:
[tex]y=0[/tex]
(d)
Answer:
A
