To determine the amplitude, period, and frequency of the given function from its graph, we can use the following definitions:
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Amplitude: The amplitude of a function \( A \) is the maximum distance from the horizontal axis to the peak (maximum value) or trough (minimum value) of the graph. It is calculated as: \[ A = \frac{\text{Maximum Value} - \text{Minimum Value}}{2} \]
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Period: The period \( P \) is the horizontal length of one complete cycle of the graph. For trigonometric functions such as sine and cosine, it is typically found by observing the interval over which the function completes one cycle.
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Frequency: The frequency \( f \) is the number of complete cycles the function completes in a unit interval, and is related to the period by the formula: \[ f = \frac{1}{P} \]
Now, we can analyze the statements provided:
- The function has a period of \( 2\pi \).
- The function has a period of \( 1 \).
- The function has a frequency of \( \pi \).
- The function has an amplitude of \( 8 \).
To choose the correct option, you would ideally need to inspect the graph to find the values of amplitude, period, and frequency.
Since I can't view images or graphs directly, you would need to check:
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For Amplitude: Look for the highest and lowest points of the function. If the maximum value is 8 and the minimum value is 0, then the amplitude would be \( \frac{8 - 0}{2} = 4 \).
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For Period: Measure how long it takes for the function to complete one full cycle. If it goes from 0 to 2π, then the period is \( 2\pi \). If it goes from 0 to 1, then it's 1.
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For Frequency: Calculate using the period found. If the period is \( 2\pi \), the frequency would be \( \frac{1}{2\pi} \).
Choose the statement based on your findings from the graph:
- If you find the period is indeed \( 2\pi \), then statement 1 is correct.
- If the period is \( 1 \), then statement 2 is correct.
- If the frequency is \( \pi \), statement 3 is correct which would require a period of \( \frac{1}{\pi} \).
- If the amplitude is \( 8 \), then statement 4 is correct.
Check against your findings to select the correct statement!