Question

What is the amplitude and period of the following function?

Answer 1

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.