Question

given the equation ( y = 6\tan(3x + 6) ) the period is: the horizontal shift is: units to the select an answer add work check answer

Explanation:

Step1: Recall the formula for the period of \(y = A\tan(Bx - C)+D\)

The period of \(y = A\tan(Bx - C)+D\) is \(\frac{\pi}{|B|}\). For \(y = 6\tan(3x + 6)=6\tan(3(x + 2))\), here \(B = 3\).

$$ \text{Period}=\frac{\pi}{|3|}=\frac{\pi}{3} $$

Step2: Recall the formula for the horizontal shift of \(y = A\tan(Bx - C)+D\)

The horizontal shift of \(y = A\tan(Bx - C)+D\) is \(\frac{C}{B}\). For \(y = 6\tan(3x + 6)=6\tan(3x-(- 6))\), here \(B = 3\) and \(C=-6\).

$$ \text{Horizontal shift}=\frac{-6}{3}=- 2 $$

The negative sign indicates a shift to the left.

Answer:

The period is \(\frac{\pi}{3}\). The horizontal shift is \(2\) units to the left.