Questions: f(x)=[?] cos (□x)+□

f(x)=[?] cos (□x)+□
Transcript text: \[ f(x)=[?] \cos (\square x)+\square \]
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Solution

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Solution Steps

Step 1: Identify the amplitude

The amplitude of the function is the maximum value of the function minus the minimum value divided by 2. Here, the maximum value is 4 and the minimum value is -3. \[ \text{Amplitude} = \frac{4 - (-3)}{2} = \frac{7}{2} = 3.5 \]

Step 2: Determine the period

The period of the function is the length of one complete cycle. From the graph, one complete cycle goes from \(-\pi/2\) to \(\pi/2\), so the period is: \[ \text{Period} = \pi \]

Step 3: Calculate the frequency

The frequency \(B\) is related to the period by the formula: \[ B = \frac{2\pi}{\text{Period}} = \frac{2\pi}{\pi} = 2 \]

Step 4: Identify the phase shift and vertical shift

From the graph, there is no horizontal shift (phase shift) and no vertical shift. Therefore, the phase shift is 0 and the vertical shift is 0.

Final Answer

\[ f(x) = 3.5 \cos(2x) \]

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