How do you find all the asymptotes for # (4x)/(x-3) #?

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Answer 1 · 2018-07-22T19:45:47

Vertical asymptote: #x=3# & Horizontal asymptote: #y=4#

Given function:

#f(x)={4x}/{x-3}#

Setting #x-3=0\implies x=3#

The given function is undefined at #x=3# or #x=3# is a point of discontinuity.

Hence, the given curve has a vertical asymptote: #x=3#

Now, the horizontal asymptote:

#y=\lim_{x\to \pm\infty}f(x)#

#y=\lim_{x\to \pm\infty}(\frac{4x}{x-3})#

#y=4#