Question

How do you find the asymptotes for `f(x)= (x-3)/ (x^2-3x-10)`?

Answer 1

vertical asymptotes x = -2 , x=5
horizontal asymptote y = 0

Explanation:

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

solve: `x^2-3x-10= 0 → (x-5)(x+2)=0`

`rArr x = -2 , x = 5 " are the equations "`

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

If degree of numerator is less than the degree of the denominator , as in this case, degree of numerator is 1 and degree of denominator is 2. Then the equation is y = 0.

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