function f is shown in the xy - plane. function f is an image of a parent function that has undergone a…

function f is shown in the xy - plane. function f is an image of a parent function that has undergone a midline shift. which of the following could define the graph? of(x)=sin(x - 3.25) of(x)=sin x - 3.25 of(x)=cos(x - 3.25) of(x)=cos x - 3.25

function f is shown in the xy - plane. function f is an image of a parent function that has undergone a midline shift. which of the following could define the graph? of(x)=sin(x - 3.25) of(x)=sin x - 3.25 of(x)=cos(x - 3.25) of(x)=cos x - 3.25

Answer

Explanation:

Step1: Recall mid - line shift rule

For a trigonometric function (y = A\sin(Bx - C)+D) or (y=A\cos(Bx - C)+D), the mid - line is (y = D). A mid - line shift is a vertical shift. If the parent function (y=\sin x) or (y = \cos x) (mid - line (y = 0)) is shifted vertically by (k) units, the new function is (y=\sin x + k) or (y=\cos x + k).

Step2: Analyze the given graph

The mid - line of the parent functions (y = \sin x) and (y=\cos x) is (y = 0). The graph shown has a mid - line below the (x) - axis. A vertical shift of a trigonometric function is represented by adding or subtracting a constant outside the trigonometric function. The functions (f(x)=\sin(x - 3.25)) and (f(x)=\cos(x - 3.25)) are horizontal shifts, not mid - line (vertical) shifts. The functions (f(x)=\sin x-3.25) and (f(x)=\cos x - 3.25) are vertical shifts of the parent functions (y = \sin x) and (y=\cos x) respectively. Since the graph has a shape similar to (y=\sin x) (starts at the mid - line and goes up first), the function is (f(x)=\sin x-3.25).

Answer:

(f(x)=\sin x - 3.25)