How do you find vertical and horizontal asymptotes of $(4x)/(x-3)$ ?

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Answer 1 · 2015-08-19T23:32:49

There is a vertical asymptote at $color(red)(x=3)$ and a horizontal asymptote at $color(red)(y=4)$ .

$f(x)=(4x)/(x-3)$

Step 1. Find the vertical asymptotes.

Set the denominator equal to zero and solve for $x$ .

$x-3=0$

$x=3$

There is a vertical asymptote at $x=3$ .

Step 3. Find the horizontal asymptotes.

Since the numerator and denominator are the same degree, we must divide the coefficients of the highest terms.

$4/1=4$

The horizontal asymptote is at $y=4$ .

Graph

How do you find vertical and horizontal asymptotes of (4x)/(x-3)(4x)/(x-3)?