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

Explanation:

Step1: Determine the amplitude A

The amplitude is half the vertical distance between the maximum and minimum values. The maximum value is 1 and the minimum is - 1, so $A=\frac{1 - (-1)}{2}=1$.

Step2: Determine the period and find B

The period $T$ of the sine - wave is $2\pi$. The formula for the period of $y = A\sin(Bx + C)+D$ is $T=\frac{2\pi}{|B|}$. Since $T = 2\pi$, then $\frac{2\pi}{|B|}=2\pi$, so $B = 1$.

Step3: Determine the phase - shift C

The graph passes through the origin, and for the standard sine - function $y=\sin x$ which also passes through the origin, the phase - shift $C = 0$.

Step4: Determine the vertical shift D

The mid - line of the graph is $y = 0$. So the vertical shift $D = 0$.

Answer:

$f(x)=\sin(x)$