Question

How do you find the vertical, horizontal or slant asymptotes for `3/(2x-1)`?

Answer 1

vertical asymptote `x = 1/2`
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 : 2x - 1 = 0 → `x = 1/2 " is the asymptote "`

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 of asymptote is always y = 0

Here is the graph of the function.
graph{3/(2x-1) [-10, 10, -5, 5]}