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

1 Answer
Tamir E.
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]}

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