Question

How do you find vertical, horizontal and oblique asymptotes for `(-7x + 5) / (x^2 + 8x -20)`?

Answer 1

vertical asymptotes x = - 10 , x = 2
horizontal asymptote y = 0

Explanation:

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

solve: `x^2+8x-20=0→(x+10)(x-2)=0`

`rArrx=-10,x=2" are the asymptotes "`

Horizontal asymptotes occur as `lim_(xto+-oo) , f(x) to 0`

When the degree of the numerator < degree of denominator as is the case here (numerator-degree 1 , denominator-degree 2) then the equation is always y = 0

Oblique asymptotes occur when the degree of the numerator > degree of denominator. This is not the case here hence there are no oblique asymptotes.
graph{(-7x+5)/(x^2+8x-20) [-20, 20, -10, 10]}