$\"\"$

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Observe the graph:

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$\"\"$

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The graph of a function $\"\"$ is divided into three trapezoid shapes and one rectangle.

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Trapezoid area $\"\"$ .

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Find $\"\"$ .

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$\"\"$ Sum of area.

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$\"\"$

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$\"\"$ . $\"\"$

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(b)

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The average value of $\"\"$ on interval $\"\"$ .

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Average value of the function $\"\"$ on $\"\"$ is defined as $\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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Average value of the function is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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Average value of the function is $\"\"$ .

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$\"\"$

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(c)

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The graph $\"\"$ is translated two units upward.

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Since the graph has $\"\"$ units on $\"\"$ -axis, it is translated two units upward.

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The area of $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The area $\"\"$ .

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The average value of $\"\"$ on interval $\"\"$ .

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Average value of the function is $\"\"$ .

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$\"\"$ .

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Average value is $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) Average value of the function is $\"\"$ .

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(c) $\"\"$ and average value is $\"\"$ .