find an equation for the sine graph, f(x):\nwrite your answer in the form f(x)=a sin(bx + c)+d, where a, b…

Explanation:

Step1: Determine the amplitude A

The amplitude is half the distance between the maximum and minimum values. From the graph, the maximum value is 3 and the minimum is - 3. So $A=\frac{3 - (-3)}{2}=3$.

Step2: Determine the period T and find B

The period is the horizontal distance between two consecutive peaks. From the graph, $T = 4$. Since $T=\frac{2\pi}{B}$, then $B=\frac{2\pi}{T}=\frac{2\pi}{4}=\frac{\pi}{2}$.

Step3: Determine the phase - shift C

The graph passes through the origin and has no horizontal shift, so $C = 0$.

Step4: Determine the vertical - shift D

The mid - line of the graph is $y = 0$, so $D = 0$.

Answer:

$f(x)=3\sin(\frac{\pi}{2}x)$