2. identify the period and equation of one asymptote of f(x)=tan(x)+2. then graph f(x). period: equation of…

Explanation:

Step1: Recall period formula for tangent function

The period of the tangent function $y = A\tan(Bx - C)+D$ is $T=\frac{\pi}{|B|}$. For $y = \tan(x)+2$, $B = 1$, so the period $T=\frac{\pi}{|1|}=\pi$.

Step2: Recall equation of asymptotes for tangent function

The tangent function $y=\tan(x)$ has asymptotes at $x=\frac{\pi}{2}+k\pi$, $k\in\mathbb{Z}$. For $y = \tan(x)+2$, the vertical - asymptotes have the same form. When $k = 0$, one of the asymptotes is $x=\frac{\pi}{2}$.

Answer:

Period: $\pi$ Equation of one asymptote: $x=\frac{\pi}{2}$