from the parent function y = sin(x), the function shown in the graph is shifted\no $\frac{pi}{4}$ units to…

Answer:

The function (y = \sin(x)) has a zero - point at (x = 0). In the given graph, the corresponding zero - point (the point where the graph crosses the x - axis and starts to increase) is at (x=\frac{\pi}{2}).

For a sine function (y = \sin(x - h)), a shift of (h) units to the right is represented. When comparing the zero - point of (y=\sin(x)) (at (x = 0)) and the zero - point of the given graph (at (x=\frac{\pi}{2})), the function (y=\sin(x)) is shifted (\frac{\pi}{2}) units to the right.

So the answer is (\frac{\pi}{2}) units to the right.

Explanation:

Step1: Identify key - point of parent function

The zero - point of (y = \sin(x)) is (x = 0).

Step2: Identify key - point of shifted function

The zero - point of the given function is (x=\frac{\pi}{2}).

Step3: Determine the shift

The shift is (\frac{\pi}{2}-0=\frac{\pi}{2}) units to the right.