Change the form of \(y = \dfrac {2x + 3}{x + 1}\)

\begin{equation*}
\begin{split}
y & = \frac {2x + 3}{x + 1} \\\\
y & = \frac {2(x + 1) + 1}{x + 1} \\\\
y & = 2 + \frac {1}{x + 1}
\end{split}
\end{equation*}

Asymtotes

For \(x \rightarrow \: \sim, \: y \rightarrow 2\)

Asymtote \(y = 2\)

For \(y \rightarrow \: \sim, \: x + 1 \rightarrow 0\)

Asymtote \(x = - 1\)

Axis intercept

X-intercept when y = 0

\begin{equation*}
\begin{split}
y & = \frac {2x + 3}{x + 1} \\\\
0 & = \frac {2x + 3}{x + 1} \\\\
0 & = 2x + 3 \\\\
- \frac 32 & = x
\end{split}
\end{equation*}

\((-\frac 32,0)\)

Y-intercept when x = 0

\begin{equation*}
\begin{split}
y & = \frac {2x + 3}{x + 1} \\\\
y & = \frac {0 + 3}{0 + 1} \\\\
y & = 3
\end{split}
\end{equation*}

\((0,3)\)

Graph of \(y = \dfrac {2x + 3}{x + 1}\)