Question

How do you find the vertical, horizontal or slant asymptotes for `h(x) = (2x - 1)/ (6 - x)`?

Answer 1

vertical asymptote x = 6
horizontal asymptote y = -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 : 6 - x = 0 → x = 6 is the equation

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

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

`y = 2/-1 = -2 rArr y = -2 " is the equation "`

Here is the graph of the function.
graph{(2x-1)/(6-x) [-10, 10, -5, 5]}