Question

How do you find the asymptotes for `y= (x + 1 ) / ( 2x - 4)`?

Answer 1

vertical asymptote at 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 of degree 1.Then the equation can be found by taking the ratio of leading coefficients.

equation is `y = 1/2`

Here is the graph of the function to illustrate.
graph{(x+1)/(2x-4) [-11.25, 11.25, -5.625, 5.625]}