$\"\"$

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The function is $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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So the graph of the function includes the origin point.

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Find the horizontal asymptote of function.

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Definition of a horizontal asymptote : $\"\"$ or $\"\"$ .

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$\"\"$

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The squeeze theorem :

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If $\"\"$ when $\"\"$ is near to $\"\"$ and $\"\"$ then $\"\"$ .

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Use the squeeze theorem, so find the function $\"\"$ lesser than $\"\"$ and a function $\"\"$ greater than $\"\"$ .

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The range of sine function is $\"\"$ .

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So $\"\"$ .

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Multiply $\"\"$ throughout the equation.

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$\"\"$

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$\"\"$

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By the squeeze theorem $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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By squeeze theorem, as $\"\"$ then $\"\"$ .

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Therefore $\"\"$ .

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Horizontal Asymptote is $\"\"$ .

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Observe the given graphs which has origin point in its graph and horizontal asymptote at $\"\"$ .

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So the graph $\"\"$ is the correct match to the function.

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$\"\"$

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