40. fill in the missing blanks. some info has been filled out.\nfunction: cosine\nvertical stretch/shrink…

Answer:

$y = 2\cos(6x)+5$

Explanation:

Step1: Recall general cosine - function form

$y = A\cos(Bx - C)+D$

Step2: Determine the value of A

The vertical stretch/shrink factor is $A$. Given $A = 2$.

Step3: Find the value of B

The period formula for $y=\cos(Bx)$ is $T=\frac{2\pi}{B}$. Given $T = \frac{\pi}{3}$, then $\frac{\pi}{3}=\frac{2\pi}{B}$. Solving for $B$: Cross - multiply gives $\pi B=6\pi$, so $B = 6$.

Step4: Determine the value of C

The phase - shift is given by $\frac{C}{B}$. Since the phase - shift is none, $C = 0$.

Step5: Determine the value of D

The vertical displacement is $D$. Given the vertical displacement is up 5, so $D = 5$.

Step6: Write the equation

Substitute $A = 2$, $B = 6$, $C = 0$, and $D = 5$ into $y = A\cos(Bx - C)+D$ to get $y = 2\cos(6x)+5$.