Question

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

Answer 1

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

Explanation:

`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`.