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Effectus [21]
3 years ago
5

What is the amplitude and period of the following function?

Mathematics
1 answer:
larisa [96]3 years ago
7 0

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: P = \frac{2\pi}{B}.


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 P = \frac{2\pi}{B}, and we substitute the values into the equation. The value B, is 1/3.


P = \frac{2\pi}{\frac{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.

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