home > s25 ma2090 - dambroise precalculus > assessment\nhomework #15 - phase shift and modeling\nscore…

Explanation:

Step1: Recall period formula for tangent function

The period of the tangent function $y = A\tan(Bx - C)$ is $\frac{\pi}{|B|}$. For the function $y = 7\tan(2x + 6)$, we have $B = 2$.

Step2: Calculate the period

Using the formula, the period $T=\frac{\pi}{|2|}=\frac{\pi}{2}$.

Step3: Recall horizontal - shift formula

The horizontal shift of the function $y = A\tan(Bx - C)$ is given by $\frac{C}{B}$. For the function $y = 7\tan(2x+6)=7\tan(2(x + 3))$, we can rewrite it in the form $y = A\tan(Bx - C)$ as $y = 7\tan(2x-(- 6))$. Here $B = 2$ and $C=-6$. The horizontal shift is $\frac{-6}{2}=-3$, which means 3 units to the left.

Answer:

The period is: $\frac{\pi}{2}$ The horizontal shift is: 3; units to the left