Question

How do you find the vertical, horizontal or slant asymptotes for `y = 5/(x - 1)`?

Answer 1

Horizontal asymptote: `y=0`

Explanation:

The only horizontal/slant asymptote is a horizontal asymptote at `y=0`. This is because the degree on the numerator (0) is less than the degree on the denominator (1).

Answer 2

Vertical asymptote: x = 1; and horizontal asymptote: y = 0.

Explanation:

graph{y(x-1)-5=0 [-10, 10, -5, 5]}

The general equation of a rectangular hyperbola with center at #(

alpha, beta ) and m as the slope of one of the asymptotes is

`((y-beta)-m(x-alpha)((m(y-beta)+x-alpha)` = constant.

The asymptotes are given by

`y-beta=m(x-alpha) and x-alpha + m(y-beta)=0`

Here, it is `y(x-1)=5`. So, the asymptotes are given by

#x-1=0 and y = 0.

For this answer, I recalled from my memory what I had learnt, more

than 60 years ago. The graph affirms that I am right.