Questions: Where is the graph increasing and decreasing?

Transcript text: Where is the graph increasing and decreasing?

Solution

Solution Steps

Step 1: Identify the function type

The graph appears to be a sinusoidal function, likely a sine or cosine function, given its periodic nature and the presence of maximum and minimum points.

Step 2: Determine the amplitude

The maximum value of the function is 8 and the minimum value is -8. The amplitude \(A\) is half the distance between the maximum and minimum values: \[ A = \frac{8 - (-8)}{2} = 8 \]

Step 3: Determine the period

The period \(T\) is the distance between two consecutive points where the function repeats its pattern. From the graph, the function repeats every \(2\pi\) units along the x-axis.

Final Answer

The function is of the form \( y = A \sin(Bx) \) or \( y = A \cos(Bx) \). Given the amplitude \(A = 8\) and the period \(T = 2\pi\), we have \(B = \frac{2\pi}{T} = 1\). Therefore, the function can be written as: \[ y = 8 \sin(x) \] or \( y = 8 \cos(x) \).

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