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

1 Answer
Feb 9, 2016

Answer:

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]}