Question

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

Transformations of functions
ANSWERED
asked 2021-01-31

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

Answers (1)

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
image

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