How do you find the vertical, horizontal or slant asymptotes for $y=(2x)/(x-3)$ ?

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Answer 1 · 2016-11-07T10:52:30

$color(blue)(x=3)$ is a Vertical Asymptote.

$color(blue)(y=2)$ is the Horizontal Asymptote.

$No Slant Asymptote$

Vertical Asymptote is determined by setting the denominator to zero :

$x-3=0rArrx=3$
Therefore ,

$color(blue)(x=3)$ is a Vertical Asymptote.

The degree of the numerator is the same as that of the denominator , so there is Horizontal Asymptote but no slant Asymptote .

If the numerator and denominator have the same degree

$(a x^ n +b x +c )/(a 'x ^n + b')$

Then the Horizontal Asymptote is , $a/(a')"$ ,the fraction formed by their coefficients of the highest degree.

In the given quotient ,the numerator and denominator have the same degree $1$ ,

therefore,

$color(blue)(y=2)$ is the Horizontal Asymptote.

How do you find the vertical, horizontal or slant asymptotes for y=(2x)/(x-3)y=(2x)/(x-3)?