The function is .

Substitute in .

So the graph of the function includes the origin point.

Find the horizontal asymptote of function.

Definition of  a horizontal asymptote : or .

The squeeze theorem :

If when is near to and then .

Use the squeeze theorem, so find the function lesser than and a function greater than ,

The range of sine function is .

So .

Multiply  throughout the equation.

By the squeeze theorem , and .

By squeeze theorem, as then .

Therefore .

Horizontal Asymptote is .

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

So the graph   is the correct match to the function.

The graph is the graph of the function .