Question

How do you find the asymptotes for `f(x)= (x+5)/(x+3)`?

Answer 1

vertical asymptote at x = -3
horizontal asymptote at y = 1

Explanation:

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

solve x + 3 = 0 `rArr x = - 3`

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

If the degree of the numerator and denominator are equal , the equation can be found by taking the ratio of leading coefficients. Here they are both degree 1.

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

Here is the graph of the function as an illustration.
graph{(x+5)/(x+3) [-10, 10, -5, 5]}