**Transcription of Educational Content:**Graph Analysis of Sinusoidal Function**Objective:** Provide the graph of the sinusoidal function over the interval \([0, 24]\).**Function:** \[ f(x) = 6 \cos \left( \frac{\pi}{5} (x - 3) \right) + 2 \]**Characteristics to Identify:**| Characteristic | Description ||-----------------------|-------------|| Amplitude | || Vertical Translation | || Horizontal Dilation | || Phase Shift | || Period | |**Graph Description:**The graph represents a cosine function plotted on an interval from 0 to 24. The x-axis is scaled in numeric radians with \(\pi\) approximately equal to 3.14. The function demonstrates regular oscillations typical of a cosine wave. **Key Features to Analyze:**- **Amplitude:** This is the height from the middle of the wave to its peak. The graph has an amplitude of 6.- **Vertical Translation:** The graph shifts vertically by 2 units upwards.- **Horizontal Dilation:** The horizontal stretch/compression factor due to the \(\frac{\pi}{5}\) in the function.- **Phase Shift:** The graph shifts horizontally by 3 units to the right.- **Period:** The period can be calculated using the formula \( \frac{2\pi}{\text{horizontal dilation factor}} \).These elements illustrate the transformations applied to the basic cosine function, resulting in the specific wave characteristics represented on the graph.

Name: **Transcription of Educational Content:**Graph Analysis of Sinusoidal
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: **Transcription of Educational Content:**Graph Analysis of Sinusoidal Function**Objective:** Provide the graph of the sinusoidal function over the interval \([0, 24]\).**Function:** \[ f(x) = 6 \cos \left( \frac{\pi}{5} (x - 3) \right) + 2 \]**Cha