$\"\"$

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The condition are :

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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From the conditions,

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The value of the function at $\"\"$ is $\"\"$ .

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$\"\"$ represents that $\"\"$ is concave downward on $\"\"$ .

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$\"\"$ represents as $\"\"$ tends to $\"\"$ then $\"\"$ approaches to $\"\"$ .

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$\"\"$ represents as $\"\"$ tends to $\"\"$ then $\"\"$ approaches to $\"\"$ .

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$\"\"$ and $\"\"$ represents that $\"\"$ has a vertical asymptote at $\"\"$ .

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So $\"\"$ is not defined for $\"\"$ .

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Graph :

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Graph the function such that all the conditions are satisfied :

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$\"\"$

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$\"\"$

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Graph of the function satisfying all the conditions is

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$\"\"$ .