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Given the function f(x) = 1 / 2 sin ( x - π / 4), what does the amplitude represent?

a) Vertical shift
b) Horizontal shift
c) Maximum displacement from the mean
d) Period of the function

1 Answer

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Final answer:

The correct answer is option c. The amplitude in the function f(x) = 1/2 sin(x - π/4) represents the maximum displacement from the mean position, not a horizontal or vertical shift, nor the period of the function. It tells us the height of the wave's peak from the central axis.

Step-by-step explanation:

When discussing the function f(x) = \frac{1}{2} \sin (x - \frac{\pi}{4}), the amplitude represents the maximum displacement from the mean or equilibrium position to the peak or trough in a wave or oscillating system. In this sine function, the amplitude is \(\frac{1}{2}\) which tells us the height of the wave each cycle of the function will reach, both positively and negatively from the mean position.

The amplitude does not correspond to a vertical or horizontal shift or the period of the function. The period of a sine or cosine function indicates how long it takes for the function to complete one full cycle and is determined by the coefficient of x within the function. It's important to note that the amplitude is always a positive value and provides information about the intensity or level of fluctuation in harmonic motion or wave functions.

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