what is the period of the function $y = \tanleft(\frac{pi}{4}left(x-\frac{pi}{3}\right)\right)$?\n3 units\n4…

Explanation:

Step1: Recall tangent - function period formula

The period of the tangent function $y = A\tan(Bx - C)+D$ is given by $T=\frac{\pi}{|B|}$.

Step2: Identify the value of B

For the function $y=\tan\left(\frac{\pi}{4}(x - \frac{\pi}{3})\right)=\tan\left(\frac{\pi}{4}x-\frac{\pi^{2}}{12}\right)$, we have $B = \frac{\pi}{4}$.

Step3: Calculate the period

Using the formula $T=\frac{\pi}{|B|}$, substitute $B=\frac{\pi}{4}$ into it. Then $T=\frac{\pi}{\frac{\pi}{4}}$. Since $\frac{\pi}{\frac{\pi}{4}}=\pi\times\frac{4}{\pi}=4$.

Answer:

4 units