Answer:
Step-by-step explanation:
The function to be analyzed is:
[tex]y = \frac{4}{x-1}+5[/tex]
This function has a vertical and a horizontal asymptote. The vertical asymptote is located where discontinuity exist. That is:
[tex]x = 1[/tex]
Besides, the horizontal asymptote coincides with the limit of function, which is:
[tex]\lim_{x \to \pm \infty} \left(\frac{4}{x-1} + 5\right)[/tex]
[tex]\lim_{x \to \infty} \frac{4}{x-1} + \lim_{x \to \infty} 5[/tex]
[tex]L = 0 + 5[/tex]
[tex]L = 5[/tex]
The horizontal asymptote is:
[tex]y = 5[/tex]
The function and the asymptotes are presented in the image attached below.
