What are the asymptotes and removable discontinuities, if any, of f(x)= (3-5x)/( x+2x^2)?

1 Answer
Nov 21, 2017

vertical asymptotes are x=0 and x=-1/2
horizontal asymptote is y=0

Explanation:

Let 3-5x=0
=> x_u=3/5

Let x+2x^2=0
=> x_(d_1)=0 or x_(d_2)=-1/2

=>
x_u!=x_(d_1)!=x_(d_2)

=>
vertical asymptotes are x=0 and x=-1/2

lim_(x rarr +-oo)f_((x))=0
=>
horizontal asymptote is y=0

graph{(3-5x)/(x+2x^2) [-12.63, 12.69, -6.3, 6.36]}