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.\ng(x)=a sin(x + c)+d
Answer
Explanation:
Step1: Determine the vertical - stretch factor
The vertical stretch factor $A$ is the multiplier of the function. A vertical stretch by a factor of 3 means $A = 3$.
Step2: Determine the horizontal - shift value
For a horizontal shift of the function $y=\sin(x)$ to the left by $h$ units, the transformation is $y = \sin(x + h)$. Here, $h=\frac{\pi}{2}$, so $C=\frac{\pi}{2}$.
Step3: Determine the vertical - shift value
A vertical shift down by $k$ units of the function $y = f(x)$ is given by $y=f(x)-k$. Here, a vertical shift down 4 units means $D=-4$.
Answer:
$g(x)=3\sin(x + \frac{\pi}{2})-4$