Question

How do you find the asymptotes for `f(x)=(-7x + 5) / (x^2 + 8x -20)`?

Answer 1

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

Explanation:

The denominator of f(x) cannot be zero as this would be undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values of x then they are vertical asymptotes.

solve: `x^2+8x-20=0rArr(x+10)(x-2)=0`

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

Horizontal asymptotes occur as

`lim_(xto+-oo),f(x)toc" (a constant)"`

divide terms on numerator/denominator by the highest power of x, that is `x^2`

`((-7x)/x^2+5/x^2)/(x^2/x^2+(8x)/x^2-20/x^2)=(-7/x+5/x^2)/(1+8/x-20/x^2)`

as `xto+-oo,f(x)to(0+0)/(1+0-0)`

`rArry=0" is the asymptote"`
graph{(7x+5)/(x^2+8x-20) [-40, 40, -20, 20]}