write the equation of the trigonometric function shown in the graph. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Determine the amplitude

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

Step2: Find the period

The period $T$ is the distance between two consecutive peaks. From the graph, $T=\frac{\pi}{2}-(-\frac{\pi}{2})=\pi$. Using the formula $T = \frac{2\pi}{B}$, we can solve for $B$. Since $T=\pi$, then $\pi=\frac{2\pi}{B}$, and $B = 2$.

Step3: Check the phase - shift and vertical - shift

The graph passes through the origin $(0,0)$, so there is no phase - shift ($C = 0$) and no vertical - shift ($D=0$). The general form of a sine function is $y = A\sin(Bx - C)+D$.

Answer:

$y = 2\sin(2x)$