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

##### 1 Answer

Feb 9, 2016

vertical asymptote

# x = -1/2 #

horizontal asymptote# y = -5/2#

#### Explanation:

vertical asymptotes occur when the denominator of a rational function tends to zero.

To find the equation

solve 1 + 2x = 0

# rArr x = -1/2 # horizontal asymptotes occur as

# lim_(x→±∞) f(x) → 0# If the degree of the numerator an denominator are equal then the equation can be found by taking the ratio of leading coefficients

in this case they are both of degree 1

I'll rewrite f(x) to assist in finding leading coefficients

f(x)

#= (-5x+1)/(2x+ 1 ) # equation of asymptote:

# y = -5/2 # here is the graph of f(x)

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