Question

Give the equation of the horizontal asymptote of the function shown below. g(x) 2x/ x+5 O A. y = 2 O B. y=-5 C. X = 2 OD. y = 2/5

Answer 1

Given:

The function is,

$g(x)=\frac{2x}{x+5}$

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,

$\begin{gathered} \lim _{x\to\infty}g(x)=\lim _{x\to\infty}(\frac{2x}{x+5}) \\ =\lim _{x\to\infty}(\frac{2x}{x(1+\frac{5}{x})}) \\ =\lim _{x\to\infty}\frac{2}{1+\frac{5}{x}} \\ =2 \\ \text{Similarly when x}\rightarrow-\infty,g(x)=2 \end{gathered}$

So, the equation for the horizontal asymtotes is y = 2.

Answer: Option A) y = 2.