Option C: [tex]x=-4[/tex] , [tex]y=2[/tex] is the asymptotes of the equation.
Explanation:
The equation is [tex]f(x)=\frac{2x}{x+4}[/tex]
The vertical asymptote of the equation can be determined by equating the denominator of the equation to zero.
Thus, we have,
[tex]x+4=0[/tex]
[tex]x=-4[/tex]
Hence, the vertical asymptote of the function is [tex]x=-4[/tex]
Now, we shall determine the horizontal asymptote.
The horizontal asymptote of the function can be determined by dividing the leading coefficient of x in the numerator by the leading coefficient of x in the denominator.
Thus, we have,
[tex]y=\frac{2}{1}[/tex]
[tex]y=2[/tex]
Hence, the horizontal asymptote of the function is [tex]y=2[/tex]
Therefore, Option C is the correct answer.
