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The absolute value function is $\"\"$ .

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Observe the graph:

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There are two translations.

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First translation is horizontal translation.

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The graph of $\"\"$ is the graph of $\"\"$ translated.

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$\"\"$ units right when $\"\"$ , and $\"\"$ units left when $\"\"$ .

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Here $\"\"$ .

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The graph of $\"\"$ translated $\"\"$ units to the left.

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Second translation is vertical translation.

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The graph of $\"\"$ is the graph of $\"\"$ translated.

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$\"\"$ units up when $\"\"$ , and $\"\"$ units down when $\"\"$ .

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Here $\"\"$ .

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The graph of $\"\"$ translated $\"\"$ units down.

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The graph of $\"\"$ is the graph of $\"\"$ translated $\"\"$ units to the left and $\"\"$ units down.

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The equation is $\"\"$

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$\"\"$ .