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

1 Answer
Jul 28, 2016

Answer:

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]}