The text in the image reads: --- The function graphed is of the form \( y = a \sin bx \) or \( y = a \cos bx \), where \( b > 0 \). Determine the equation of the graph. --- **Graph Description:** The graph displays a trigonometric wave that consists of three complete cycles from left to right. The wave is symmetrical and evenly spaced along the x-axis. The maximum value of the graph is 5, and the minimum value is 1, indicating an amplitude of 2. The period of the wave, the distance of one complete cycle along the x-axis, appears to be approximately 2 units for each cycle. **Key Features:** - **Amplitude**: The peak height (from the center to the maximum) is 2. - **Midline**: The horizontal line at \( y = 3 \), equidistant from the maximum and minimum values. - **Period**: Each cycle appears to have a length of 2 units on the x-axis. **Conclusion:** Given the form \( y = a \sin bx \) or \( y = a \cos bx \), the equation of the graph can be determined by identifying the amplitude, period, and midline shift. Since the graph resembles a cosine function (starting at a peak), it is likely of the form \( y = a \cos bx + d \), where \( a = 2 \), \( b = \pi \), and \( d = 3 \). Therefore, the equation of the graph is approximately: \[ y = 2 \cos(\pi x) + 3 \] The image depicts a trigonometric graph of the function \(y = 3\sin(x)\). **Graph Analysis:** - **Axes:** - The horizontal axis represents the variable \(x\), marked with intervals including \(-\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), and \(2\pi\). - The vertical axis represents the \(y\)-values, scaling from \(-5\) to \(5\). - **Waveform:** - The sine wave oscillates between \(3\) and \(-3\). - The wave completes one full cycle from \(-\pi/2\) to \(3\pi/2\). - Peaks occur at \(y = 3\) and troughs at \(y = -3\). - **Period and Amplitude:** - The period of the sine wave is \(2\pi\). - The amplitude of the wave is \(3\), which is the absolute value of the coefficient in front of the sine function. This graph illustrates how changing the amplitude affects the height of the sine wave, while the period remains the same, as determined by the function's form.