question\nwrite the equation of the trigonometric function shown in the graph.

Explanation:

Step1: Determine the amplitude

The amplitude $A$ is half the distance between the maximum and minimum values. The maximum value is $4$ and the minimum is $- 4$, so $A=\frac{4 - (-4)}{2}=4$.

Step2: Determine the period

The period $T$ is the horizontal distance between two consecutive peaks. Here, $T=\pi$. Since the formula for the period of a trig - function $y = A\sin(Bx - C)+D$ or $y = A\cos(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$, and $T = \pi$, then $\pi=\frac{2\pi}{|B|}$, so $|B| = 2$.

Step3: Determine the phase - shift and vertical - shift

The graph passes through the origin $(0,0)$, and there is no vertical shift ($D = 0$) and no phase - shift ($C = 0$). Since the graph starts at the origin and has a shape like a sine function (starts at the mid - line and increases), the function is of the form $y=A\sin(Bx)$.

Answer:

$y = 4\sin(2x)$