find the period and horizontal shift of the function. h(x) = 2 sec(π/3(x + 4)) period horizontal shift

Explanation:

Step1: Recall period formula for secant

For $y = A\sec(B(x - C))$, period $T=\frac{2\pi}{|B|}$. Here $B = \frac{\pi}{3}$.

Step2: Calculate the period

$T=\frac{2\pi}{\left|\frac{\pi}{3}\right|}=\frac{2\pi}{\frac{\pi}{3}} = 6$.

Step3: Recall horizontal - shift formula

For $y = A\sec(B(x - C))$, the horizontal shift is $C$. The function is $h(x)=2\sec\left(\frac{\pi}{3}(x + 4)\right)=2\sec\left(\frac{\pi}{3}(x-(- 4))\right)$.

Answer:

period: 6 horizontal shift: -4