Question

# Use long division to rewrite the equation for g in the formtext{quotient}+frac{remainder}{divisor}

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.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}$$

2021-02-01

Step 1
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}$$
$$\begin{array} \\ &3 \\ \hline \underline{x\ +\ 2|} & 3x & -7 \\ & \ominus3x & \ominus-6 \\ \hline & & -1 \end{array}$$
The quotient is 3 and the remainer is $$\displaystyle{\frac{{-{1}}}{{{x}-{2}}}}$$
$$g(x)=3-\frac{1}{x-2}$$
We can graph g by horizontal shifting f 2 units right then vertical shifting 3 units up and reflect about y-axis.
Step 2

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