Question

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

Answer 1

Given:

The function is:

$f(x)=\dfrac{2x}{x+4}$

To find:

The vertical and horizontal asymptotes of the given function.

Solution:

We have,

$f(x)=\dfrac{2x}{x+4}$

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:

$y=\dfrac{a}{b}$

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:

$y=\dfrac{2}{1}$

$y=2$

Therefore, the correct option is C.