what are the period and phase shift for f(x) = tan(2x + π)?\n a period: π/2; phase shift: x = -π/2\n b…

Explanation:

Step1: Recall period formula for tangent

The general form of a tangent - function is $y = A\tan(Bx - C)+D$, and its period is given by $T=\frac{\pi}{|B|}$. For the function $f(x)=\tan(2x+\pi)=\tan(2x - (-\pi))$, here $B = 2$. $T=\frac{\pi}{|2|}=\frac{\pi}{2}$

Step2: Recall phase - shift formula

The phase - shift of the function $y = A\tan(Bx - C)+D$ is given by $\frac{C}{B}$. For the function $f(x)=\tan(2x+\pi)=\tan(2x - (-\pi))$, $B = 2$ and $C=-\pi$. Phase - shift $=\frac{-\pi}{2}$

Answer:

A. Period: $\frac{\pi}{2}$; phase shift: $x =-\frac{\pi}{2}$