Question

How do you find the asymptotes for `f(x)=x/(x-7)`?

Answer 1

vertical asymptote x = 7 , horizontal asymptote y = 1

Explanation:

Find vertical asymptotes when denominator of a

rational function is zero.

so equate : x - 7 = 0 → x = 7

If the degree of the numerator and the degree of the

denominator are equal a horizontal asymptote exists.

Here they are both of degree 1 and so equal.

To obtain equation take the ratio of coefficients of
leading terms.

hence `y = 1/1 rArr y = 1`

The graph illustrates these.

graph{x/(x-7) [-10, 10, -5, 5]}