Question

How to find the asymptotes of `y = (7x-5)/(2-5x)` ?

Answer 1

Explanation is given below.

Explanation:

`y=(7x-5)/(2-5x)`

To find the vertical asymptote equate the denominator to zero.

`2-5x=0`

`=>-5x=-2`
`=>x=-2/-5`
`=>x=2/5`

`x=2/5` is the equation of the vertical asymptote.

For finding the Horizontal asymptotes, we start by comparing the degrees of the numerator and denominator.

If the degree of the numerator is greater than the degree of the denominator then there is no Horizontal Asymptote.

If the degree of the numerator is lesser than the degree of the denominator then `y=0` is the horizontal asymptote.

If the degree of the numerator equals the degree of the denominator then the horizontal asymptote is given by

`y= "Lead Coefficient of the Numerator"/"Lead Coefficient of the Denominator"`

In our problem the both numerator and denominator have the degree of `1`. Therefore, the Horizontal Asymptote is

`y=7/-5`

`y=-7/5` Horizontal Asymptote