Question

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

Answer 1

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]}