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Hello!
Amplitude is the maximum displacement on the graph of a function.
Period is the displacement of x at which the graph of a function begins to repeat.
We can find the period of a circular function by using the formula: .
The amplitude is 6 because it causes the displacement of the graph to change. Therefore, the domain becomes -6 ≥ x ≥ 6.
To find the period, we use the formula , and we substitute the values into the equation. The value B, is 1/3.
This can be simplified into 6π.
Since the periodicity is 6π, the graph hits the x-axis at intervals of 3π and -3π, and the graph also hits the x-axis at the origin.
Therefore, the amplitude of the function is 6, the period is 6π, and the function hits the x-axis during intervals of 3π.
