# How do you find the asymptotes for #f(x)=(1-5x)/(1+2x)#?

##### 1 Answer

Jul 10, 2016

vertical asymptote

horizontal asymptote

#### Explanation:

The denominator of f(x) cannot equal zero. This would give division by zero which is undefined. Setting the denominator equal to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: 1 + 2x =0

#rArrx=-1/2" is the asymptote"# Horizontal asymptotes occur as

#lim_(xto+-oo),f(x)toc" (a constant)"# divide terms on numerator/denominator by x

#(1/x-(5x)/x)/(1/x+(2x)/x)=(1/x-5)/(1/x+2)# as

#xto+-oo,f(x)to(0-5)/(0+2)#

#rArry=-5/2" is the asymptote"#

graph{(1-5x)/(1+2x) [-10, 10, -5, 5]}