Question

How do you find vertical, horizontal and oblique asymptotes for `(x+3)/(x-1)`?

Answer 1

vertical asymptote x = 1
horizontal asymptote y = 1

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 asymptote

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

divide all terms on numerator/ denominator by x

`(x+3)/(x-1) = (x/x + 3/x)/(x/x -1/x) = (1 + 3/x)/(1 - 1/x)`

as x → ∞ , `3/x" and " 1/x → 0`

`rArr " equation of asymptote is " y = 1`

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