Answer :
Given:
The function is:
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
To find:
The vertical and horizontal asymptotes of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
For vertical asymptotes, equate the denominator and 0.
[tex]x+4=0[/tex]
[tex]x+4-4=0-4[/tex]
[tex]x=-4[/tex]
So, the vertical asymptote of the given function is [tex]x=-4[/tex].
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:
[tex]y=\dfrac{a}{b}[/tex]
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:
[tex]y=\dfrac{2}{1}[/tex]
[tex]y=2[/tex]
Therefore, the correct option is C.