Question

For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x minus five divided by the quantity x squared minus one

Answer 1

Explanation:

The function is:

x - 5

f(x) = ---------------

x^2 - 1

Horizontal asymptote: observe that as x grows towards infinity, the function (and graph) approaches y = 0. This is the horizontal asymptote.

Vertical asymptote: These occur whenever the denominator of a rational function becomes zero. Here the vertical asymptotes are x = ± 1.