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The function is $\"\"$ .

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Basic function is $\"\"$ .

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There are two stages obtain the graph of $\"\"$ from basic function $\"\"$ .

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Shift 1: From $\"\"$ to $\"\"$ .

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$\"\"$ , shift the graph of $\"\"$ $\"\"$ units to the right.

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Replace $\"\"$ by $\"\"$ .

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The points $\"\"$ are on $\"\"$ .

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Therefore, $\"\"$ are on $\"\"$ .

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$\"\"$

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Observe the graph:

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The graph of $\"\"$ is identical to $\"\"$ except that it is horizontally shifted $\"\"$ unit to the right.

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Shift 2: From $\"\"$ to $\"\"$ .

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$\"\"$ , shift the graph of $\"\"$ $\"\"$ units up.

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Replace $\"\"$ by $\"\"$ .

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The points $\"\"$ are on $\"\"$ .

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Therefore, $\"\"$ are on $\"\"$ .

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$\"\"$

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Observe the graph:

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The graph of $\"\"$ is identical to $\"\"$ except that it is vertically shifted up $\"\"$ units.

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The domain of the $\"\"$ is all real numbers.

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Domain of $\"\"$ in the interval notation: $\"\"$ .

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Range of $\"\"$ is all real numbers.

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Range of $\"\"$ in the interval notation: $\"\"$ .

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Graph:

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$\"\"$

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Domain of $\"\"$ in the interval notation: $\"\"$ .

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Range of $\"\"$ in the interval notation: $\"\"$ .