Question

Sketch the asymptotes and graph the function y=4/(x-1)+5​

Answer 1

Explanation:

The function to be analyzed is:

`y = (4)/(x-1)+5`

This function has a vertical and a horizontal asymptote. The vertical asymptote is located where discontinuity exist. That is:

`x = 1`

Besides, the horizontal asymptote coincides with the limit of function, which is:

`\lim_(x \to \pm \infty) \left((4)/(x-1) + 5\right)`

`\lim_(x \to \infty) (4)/(x-1) + \lim_(x \to \infty) 5`

`L = 0 + 5`

`L = 5`

The horizontal asymptote is:

`y = 5`

The function and the asymptotes are presented in the image attached below.