Which statement accurately describes how adding a number, $$ n $$, to the function $$ f(x)=\sin (x) $$ affects its graph? There is a vertical shift of $$ n $$ units. The $$ x $$-intercepts will shift $$ n $$ units. There is a change in amplitude of $$ n $$ units. The range will change by a factor of $$ 2 n $$ units.

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1. The function is given by $$ f(x)=\sin(x) $$.

2. Adding a number $$ n $$ to the function gives:
   $$
   f(x) = \sin(x) + n
   $$

3. This transformation results in each point on the graph of $$ \sin(x) $$ being moved vertically by $$ n $$ units. Thus, the entire graph shifts upward by $$ n $$ units if $$ n $$ is positive, and downward by $$ n $$ units if $$ n $$ is negative.

4. The other options are incorrect:
   - The $$ x $$-intercepts do not shift by $$ n $$ units; only their vertical position changes.
   - The amplitude remains $$ 1 $$ since adding $$ n $$ only translates the graph vertically.
   - The range does not change by a factor of $$ 2n $$; it simply shifts to $$[n-1, n+1]$$.

The correct statement is: There is a vertical shift of $$ n $$ units.
Adding $$ n $$ to $$ \sin(x) $$ moves the graph up or down by $$ n $$ units.

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