$\"\"$

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The function is $\"\"$ .

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This function represents a transformation of the graph of $\"\"$ .

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The transformation of function general form is $\"\"$ .

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Thus, here

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$\"\"$ , the graph is stretches vertically and reflected across the $\"\"$ -axis.

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$\"\"$ , the graph is shifted $\"\"$ units right.

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$\"\"$ , the graph is translated $\"\"$ units down.

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Graph:

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Graph the function $\"\"$ .

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$\"\"$

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Observe the graph:

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Domain is $\"\"$ .

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Range is $\"\"$ .

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$\"\"$

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Identify the asymptotes.

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Identify the $\"\"$ -values for $\"\"$ is undefined.

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$\"\"$

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$\"\"$ is not defined for value of $\"\"$ .

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Thus, there is an asymptote at $\"\"$ .

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From $\"\"$ , as a $\"\"$ -values decrease, $\"\"$ -values approach $\"\"$ , and as $\"\"$ -values increase, $\"\"$ -values approach $\"\"$ .

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Thus there is an asymptote at $\"\"$ .

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$\"\"$

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Graph of the function $\"\"$ is \ \

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$\"\"$

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The domain is $\"\"$ and the range is $\"\"$ .

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The asymptote at $\"\"$ .