How do you find all the asymptotes for $\frac{4 x}{x - 3}$ $(4x)/(x-3)$ ?

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Answer 1 · 2018-07-22T19:45:47

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

Given function:

$f (x) = \frac{4 x}{x - 3}$ $f(x)={4x}/{x-3}$

Setting $x - 3 = 0 \Rightarrow x = 3$ $x-3=0\implies x=3$

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

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

Now, the horizontal asymptote:

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

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

$y=4$

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