Step 1

\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}\ +\ {7}}}{{{\left\lbrace{x}\ +\ {3}\right\rbrace}}}}\)

\(\begin{array} & 2 & \\ \hline \underline{x\ +\ 3|} & 2x & +7 \\ & \ominus2x & \ominus+6 \\ \hline & & 1 \end{array}\)

The quotient is 2 and the remainder is \(\displaystyle{\frac{{{1}}}{{{x}\ +\ {3}}}}\)

\(\displaystyle{g{{\left({x}\right)}}}={2}\ +\ {\frac{{{1}}}{{{x}\ +\ {3}}}}\) We can graph g by horizontal shifting f 3 units left then vertical shifting 2 units up

Step 2