Question

How do you find the vertical, horizontal or slant asymptotes for `(x + 1 )/( 2x - 4)`?

Answer 1

vertical asymptote x = 2
horizontal asymptote `y = 1/2`

Explanation:

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

solve : 2(x-2) = 0 → x = 2 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 degree 1 then the equation can be found by taking the ratio of leading coefficients.

`rArr " equation is " y = 1/2`
Here is the graph of the function to illustrate them
graph{(x+1)/(2x-4) [-10, 10, -5, 5]}