Question

How do you find the asymptotes for `y = 4/(x - 3)`?

Answer 1

vertical asymptote at x = 3
horizontal asymptote at y = 0

Explanation:

vertical asymptotes occur as the denominator of a rational function >tends to zero. To find the equation let the denominator = 0

solve : x - 3 = 0 → x = 3 is the equation

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

If the degree of the numerator is less than the degree of the denominator , as is the case here , then the equation is y = 0

here is the graph of the function as an illustration
graph{4/(x-3) [-10, 10, -5, 5]}