enter the correct answer in the box.\nfunction g is the result of these transformations on the parent sine…

enter the correct answer in the box.\nfunction g is the result of these transformations on the parent sine function:\n- vertical stretch by a factor of 3\n- horizontal shift left $\frac{pi}{2}$ units\n- vertical shift down 4 units\nsubstitute the values of a, c, and d to complete the equation modeling function g.\n$g(x)=asin(x + c)+d$

enter the correct answer in the box.\nfunction g is the result of these transformations on the parent sine function:\n- vertical stretch by a factor of 3\n- horizontal shift left $\frac{pi}{2}$ units\n- vertical shift down 4 units\nsubstitute the values of a, c, and d to complete the equation modeling function g.\n$g(x)=asin(x + c)+d$

Answer

Answer:

$g(x)=3\sin(x + \frac{\pi}{2})- 4$

Explanation:

Step1: Determine vertical stretch factor

The vertical stretch factor $A$ is 3 as given in the transformation.

Step2: Determine horizontal - shift value

The horizontal shift is left $\frac{\pi}{2}$ units. In the form $y = A\sin(x + C)+D$, for a left - shift of $h$ units, $C = h$. So $C=\frac{\pi}{2}$.

Step3: Determine vertical - shift value

The vertical shift is down 4 units. In the form $y = A\sin(x + C)+D$, for a down - shift of $k$ units, $D=-k$. So $D = - 4$.