Question

How do you find the vertical, horizontal or slant asymptotes for `g(x)=(x+3) /( x(x-5))`?

Answer 1

vertical asymptotes x = 0 , x = 5
horizontal asymptote y = 0

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(x-5) = 0 → x = 0 , x=5 are the equations.

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, numerator degree 1 and denominator degree 2, then the equation is y = 0.

`rArr y = 0 " is the equation "`

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