Question

# Use long division to rewrite the equation for g in the formtext{quotient}+frac{remainder}{divisor}Then use this form of the function's equation and

Transformations of functions

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$

2020-12-22

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