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The function is $\"\"$ .

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(a)

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Graph the functions $\"\"$ and $\"\"$ .

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Find the simplifying form of the functions $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Graph the functions $\"\"$ :

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$\"\"$

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(b)

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A flat tax of $10000 per day be tax is $\"\"$ .

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A tax of $\"\"$ on profits is $\"\"$ .

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Observe the graph:

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Since $\"\"$ has maximum value, select the option 2 $\"\"$ tax.

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$\"\"$ tax.

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(c) The function $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ is the graph of $\"\"$ shifted down vertically $\"\"$ units.

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$\"\"$

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$\"\"$

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$\"\"$ is the graph of $\"\"$ vertically compressed by a factor of $\"\"$ .

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$\"\"$ is the graph of $\"\"$ shifted down vertically $\"\"$ units. $\"\"$ is the graph of $\"\"$ vertically compressed by a factor of $\"\"$ .

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(d)

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The government offered the options of a flat tax of $\"\"$ or a tax of $\"\"$ on profits.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Graph the functions $\"\"$ and $\"\"$ .

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$\"\"$

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Obsreve the graph:

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Since $\"\"$ has maximum value, select the option 2 $\"\"$ tax.

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(a) Graph of the functions $\"\"$ on same window:

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$\"\"$

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(b) $\"\"$ tax.

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(c)

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$\"\"$ is the graph of $\"\"$ shifted down vertically $\"\"$ units. $\"\"$ is the graph of $\"\"$ vertically compressed by a factor of $\"\"$ .

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(d) $\"\"$ tax.