find the period. y = -5 tan(3πx)

Explanation:

Step1: Recall tangent - period formula

For the tangent function (y = A\tan(Bx - C)+D), the period (T=\frac{\pi}{|B|}).

Step2: Identify the value of B

In the function (y=- 5\tan(3\pi x)), we have (B = 3\pi).

Step3: Calculate the period

Substitute (B = 3\pi) into the period formula (T=\frac{\pi}{|B|}), so (T=\frac{\pi}{|3\pi|}=\frac{1}{3}).

Answer:

(\frac{1}{3})