Question

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

Answer 1

vertical asymptote x = 1
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 : x - 1 = 0 → x = 1 is the equation

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 . Then 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)/(x-1) [-10, 10, -5, 5]}