lesson 18.2 checkpoint\nonce you have completed the above problems and checked your solutions, complete the…

lesson 18.2 checkpoint\nonce you have completed the above problems and checked your solutions, complete the lesson checkpoint below.\ncomplete the lesson reflection above circling your current understanding of the learning goal.\n1. what is the period of the function given?\na π/2\nb π\nc 2π\n2. which of the following is the function of the graph?\na f(x)=tan(1/2 x)\nb f(x)=tan(2x)\nc f(x)=2tan(x)

lesson 18.2 checkpoint\nonce you have completed the above problems and checked your solutions, complete the lesson checkpoint below.\ncomplete the lesson reflection above circling your current understanding of the learning goal.\n1. what is the period of the function given?\na π/2\nb π\nc 2π\n2. which of the following is the function of the graph?\na f(x)=tan(1/2 x)\nb f(x)=tan(2x)\nc f(x)=2tan(x)

Answer

Explanation:

Step1: Recall period formula for tangent function

The period of the tangent function $y = A\tan(Bx)$ is $T=\frac{\pi}{|B|}$.

Step2: Determine period from graph

From the graph, we can see that the distance between two consecutive vertical - asymptotes is $\pi$. So the period of the function is $\pi$.

Step3: Find the function of the graph

We know the period $T = \pi=\frac{\pi}{|B|}$, solving for $B$ gives $|B| = 1$. Also, the standard - form of the tangent function is $y=\tan(Bx)$. Looking at the shape and the period, for the function $y = \tan(Bx)$, when $B = 2$, the period is $\frac{\pi}{2}$, when $B=\frac{1}{2}$, the period is $2\pi$, and when $B = 1$ the period is $\pi$. The function of the graph is $y=\tan(2x)$ as it has the correct period and shape.

Answer:

  1. B $\pi$
  2. B $f(x)=\tan(2x)$