Given the function:
[tex]f(x)=\frac{2x+1}{x}[/tex]
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:
[tex]\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}[/tex]
