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.

Adding a number \( n \) to the function \( f(x)=\sin(x) \) results in a vertical shift of \( n \) units. This means that every point on the sine wave will move up (if \( n \) is positive) or down (if \( n \) is negative) the same distance, but the shape of the sine wave remains the same! Furthermore, this addition does not affect the amplitude of the sine function, which remains 1. Therefore, the \( x \)-intercepts will simply move to new positions depending on the value of \( n \), but they won’t shift evenly by \( n \) units; instead, they will either be above or below the x-axis depending on \( n \).