# What are the asymptotes of #f(x)=(1-5x)/(1+2x)#?

##### 1 Answer

Jul 29, 2017

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator 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 verical asymptote.

#"solve "1+2x=0rArrx=-1/2" is the asymptote"#

#"horizontal asymptotes occur as"#

#lim_(xto+-oo),f(x)to c" ( a constant)"#

#"divide terms on numerator/denominator by " x#

#f(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"#