Question

How do you find the vertical, horizontal or slant asymptotes for `y=4/(x+4 )`?

Answer 1

vertical asymptote x= -4
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 + 4 = 0 → x = -4 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 in this case , numerator degree 0, denominator degree 1 then the equation is always y = 0.

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