Question

How do you find the asymptotes for `y = x/(x-6)`?

Answer 1

vertical asymptote x = 6
horizontal asymptote y = 1

Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve: x - 6 = 0 → x = 6 is the equation.

Horizontal asymptotes occur as `lim_(x→±∞) f(x) → 0`

If the degree of the numerator and denominator are equal , as in this question , both of degree 1 , then the equation can be found by taking the ratio of leading coefficients.

`y = 1/1 = 1 rArr y = 1 " is the equation "`

here is the graph of the function as an illustration.
graph{x/(x-6) [-20, 20, -10, 10]}