4 multiple choice 1 point describe how the graph of y = 3 sin θ + 2 compares to y = sin θ. stretched…

4 multiple choice 1 point describe how the graph of y = 3 sin θ + 2 compares to y = sin θ. stretched vertically by a factor of 3 and shifts up 2 units stretched vertically by a factor of 2 and shifts up 3 units stretched horizontally by a factor of 2 and shifts up 3 units stretched horizontally by a factor of 3 and shifts up 2 units

4 multiple choice 1 point describe how the graph of y = 3 sin θ + 2 compares to y = sin θ. stretched vertically by a factor of 3 and shifts up 2 units stretched vertically by a factor of 2 and shifts up 3 units stretched horizontally by a factor of 2 and shifts up 3 units stretched horizontally by a factor of 3 and shifts up 2 units

Answer

Answer:

A. Stretched vertically by a factor of 3 and shifts up 2 units

Explanation:

Step1: Analyze vertical stretch

For a function $y = A\sin\theta$, when $A> 1$, it causes a vertical stretch. Here $A = 3$ in $y=3\sin\theta + 2$, so there is a vertical stretch by a factor of 3 compared to $y = \sin\theta$.

Step2: Analyze vertical shift

For a function $y=\sin\theta + k$, when $k>0$, it shifts the graph up by $k$ units. Here $k = 2$ in $y = 3\sin\theta+2$, so the graph shifts up 2 units.