Question

Determine the equations of the vertical and horizontal asymptotes, if any, for

Answer 1

Given:

The function is:

`f(x)=(2x)/(x+4)`

To find:

The vertical and horizontal asymptotes of the given function.

Solution:

We have,

`f(x)=(2x)/(x+4)`

For vertical asymptotes, equate the denominator and 0.

`x+4=0`

`x+4-4=0-4`

`x=-4`

So, the vertical asymptote of the given function is
`x=-4`.

The degree of the numerator is 1 and the degree of the denominator is also 1.

Since the degrees of numerator and denominator are equal, therefore the horizontal asymptote is:

`y=(a)/(b)`

Where, a is the leading coefficient of numerator and b is the leading coefficient of denominator.

Leading coefficient of numerator is 2 and the leading coefficient of denominator is 1, so the horizontal asymptote is:

`y=(2)/(1)`

`y=2`

Therefore, the correct option is C.