How do you determine the vertical and horizontal asymptotes of the graph of each function $f(x) = (3x)/(x+4)$ ?

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Answer 1 · 2015-08-19T23:09:11

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

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

Step 1. Find the vertical asymptotes.

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

$x+4=0$

$x=-4$

There is a vertical asymptote at $x=-4$ .

Step 3. Find the horizontal asymptotes.

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

$3/1=3$

The horizontal asymptote is at $y=3$ .

Graph

How do you determine the vertical and horizontal asymptotes of the graph of each function f(x) = (3x)/(x+4)f(x) = (3x)/(x+4)?