Given:
The function is,
[tex]g(x)=\frac{2x}{x+5}[/tex]
Horizontal asymtotes: it helps to describe the behavior of a graph as the input of function gets very large or very small.
The horizontal asymtotes for the given function is,
[tex]\begin{gathered} \lim _{x\to\infty}g(x)=\lim _{x\to\infty}(\frac{2x}{x+5}) \\ =\lim _{x\to\infty}(\frac{2x}{x(1+\frac{5}{x})}) \\ =\lim _{x\to\infty}\frac{2}{1+\frac{5}{x}} \\ =2 \\ \text{Similarly when x}\rightarrow-\infty,g(x)=2 \end{gathered}[/tex]
So, the equation for the horizontal asymtotes is y = 2.
Answer: Option A) y = 2.
