lesson 18.3 checkpoint\nonce you have completed the above problems and checked your solutions, complete the…

lesson 18.3 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. consider the function f(x)=2cos(x - π/3)+1.\na. the graph will have a midline at y = \n b. the graph will have an amplitude of \n2. consider the function f(x)=1/4tan(x - π/3)-5.\na. the graph will be translated π/3 units:\n□ a up\n□ b down\n□ c left\n□ d right\nb. the graph will have a period of. write your answer in radian measure in terms of π

lesson 18.3 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. consider the function f(x)=2cos(x - π/3)+1.\na. the graph will have a midline at y = \n b. the graph will have an amplitude of \n2. consider the function f(x)=1/4tan(x - π/3)-5.\na. the graph will be translated π/3 units:\n□ a up\n□ b down\n□ c left\n□ d right\nb. the graph will have a period of. write your answer in radian measure in terms of π

Answer

Explanation:

Step1: Recall mid - line formula for cosine function

For a cosine function of the form $y = A\cos(B(x - C))+D$, the mid - line is $y = D$. In the function $f(x)=2\cos(x-\frac{\pi}{3}) + 1$, $D = 1$.

Step2: Recall amplitude formula for cosine function

For a cosine function $y = A\cos(B(x - C))+D$, the amplitude is $|A|$. In the function $f(x)=2\cos(x-\frac{\pi}{3}) + 1$, $A = 2$, so the amplitude is $2$.

Step3: Recall horizontal translation rule for tangent function

For a tangent function $y = A\tan(B(x - C))+D$, a positive value of $C$ in $(x - C)$ causes a right - hand translation. In the function $f(x)=\frac{1}{4}\tan(x-\frac{\pi}{3})-5$, $C=\frac{\pi}{3}$, so the graph is translated $\frac{\pi}{3}$ units to the right.

Step4: Recall period formula for tangent function

For a tangent function $y = A\tan(B(x - C))+D$, the period is $\frac{\pi}{|B|}$. In the function $f(x)=\frac{1}{4}\tan(x-\frac{\pi}{3})-5$, $B = 1$, so the period is $\pi$.

Answer:

  1. a. $y = 1$ b. $2$
  2. a. D. Right b. $\pi$