Question

How do you find the vertical, horizontal or slant asymptotes for `f(x)=(5x-15)/(2x+4)`?

Answer 1

vertical asymptote x = -2
horizontal asymptote `y = 5/2`

Explanation:

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

solve: 2x + 4 = 0 → x = - 2 is the asymptote

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

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

`rArr y = 5/2 " is the asymptote "`

Here is the graph of the function.
graph{(5x-15)/(2x+4) [-20, 20, -10, 10]}