review the graph. which statement about the graph is true? the period of the graph is 2π/3. the amplitude of…

Explanation:

Step1: Recall period formula

For $y = A\sin(Bx + C)+D$, period $T=\frac{2\pi}{|B|}$.

Step2: Analyze amplitude

Amplitude is $|A|$.

Step3: Determine domain

Domain of sine - type functions is all real numbers usually, not just from - 3 to 3.

Step4: Check reflection

Compare with $y = 3\sin(2x)$.

For the given graph: The period of a sine function $y = A\sin(Bx)$ is $T=\frac{2\pi}{B}$. If we assume the general form of the sine function for the given graph is $y = A\sin(Bx + C)+D$. From the graph, we can see that the distance between two consecutive peaks (or troughs) is $\pi$. Using the period formula $T=\frac{2\pi}{B}=\pi$, we get $B = 2$. The amplitude is the maximum distance from the mid - line to the peak or trough. The mid - line is $y = 0$ and the peak value is $y = 3$ and the trough value is $y=-3$, so the amplitude $|A| = 3$. The domain of a sine function $y=\sin(x)$ and its transformations is all real numbers, not from $-3$ to $3$. The function $y = 3\sin(2x)$ has an amplitude of 3, a period of $\pi$ and no vertical shift. The given graph has the same amplitude and period as $y = 3\sin(2x)$ but is reflected over the $x$ - axis. The equation of the given graph is $y=-3\sin(2x)$.

Answer:

The graph represents a reflection over the x - axis of the function $y = 3\sin(2x)$.