Question

Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25

Answer 1

`f(x)=(x)/(2x+1)`

The given function is a rational function

We will find the zeros of the denominator

`\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=(-1)/(2) \end{gathered}`

The end behavior of the function will be as follows:

`\begin{gathered} x\rightarrow(-(1)/(2))^-;f(x)\rightarrow\infty \\ x\rightarrow(-(1)/(2))^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow(1)/(2) \\ x\rightarrow-\infty;f(x)\rightarrow(1)/(2) \end{gathered}`

The graph of the function is as follows: