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)=(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)((2x)/(x+5)) \\ =\lim _(x\to\infty)((2x)/(x(1+(5)/(x)))) \\ =\lim _(x\to\infty)(2)/(1+(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.