Question

Can you please help me list the forms As_,_ and limits

Answer 1

Given the function:

$f(x)=\frac{2x+1}{x}$

First, the graph of the function will be as shown in the following figure:

For the given rational function, we will find the following:

Domain = ( -∞, 0 ) ∪ ( 0, ∞ )

Range = ( -∞, 2) ∪ (2, ∞ )

Increasing = Φ

Decreasing = ( -∞, 2) ∪ (2, ∞ )

All asymptotes:

Vertical asymptote: x = 0

Horizontal Asymptote: y = 2

All limits:

$\begin{gathered} \lim _{x\rightarrow-\infty}f(x)=2 \\ \lim _{x\rightarrow\infty}f(x)=2 \\ \lim _{x\rightarrow0^-}f(x)=-\infty \\ \lim _{x\rightarrow0^+}f(x)=\infty \end{gathered}$