How do you find all the asymptotes for (4x)/(x-3) 4xx3?

1 Answer

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

Explanation:

Given function:

f(x)={4x}/{x-3}f(x)=4xx3

Setting x-3=0\implies x=3x3=0x=3

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

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