which statement accurately describes how adding a number, n, to the function f(x) = sin(x) affects its…

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

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

Answer

Explanation:

Step1: Recall function - transformation rule

For a function $y = f(x)$, the transformation $y=f(x)+n$ represents a vertical - shift.

Step2: Analyze the given function

The original function is $f(x)=\sin(x)$. When we add $n$ to it, we get $y = \sin(x)+n$. According to the rule of vertical shifts, for any value of $x$, the $y$ - value of the new function $\sin(x)+n$ is $n$ units more than the $y$ - value of the original function $\sin(x)$. This means the graph of $y = \sin(x)$ is shifted vertically by $n$ units.

Answer:

There is a vertical shift of $n$ units.