question\nwrite the equation of the trigonometric function shown in the graph.\nanswer attempt 1 out of 2

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: Determine the period

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

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 ($C = 0$). A sine function with $A = 2$, $B = 2$, $C = 0$, and $D = 0$ is of the form $y=A\sin(Bx)$.

Answer:

$y = 2\sin(2x)$