write the equation of the trigonometric function shown in the graph. try whole numbers or unit fractions for…

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a cosine - function $y = A\cos(Bx)+C$ is half the distance between the maximum and minimum values of the function. The maximum value of the given function is $4$ and the minimum is $0$. So, $A=\frac{4 - 0}{2}=2$.

Step2: Determine the period

The period $T$ of a cosine - function $y = A\cos(Bx)+C$ is given by $T=\frac{2\pi}{B}$. From the graph, the period $T = 1$. So, $1=\frac{2\pi}{B}$, and solving for $B$ gives $B = 2\pi$.

Step3: Determine the vertical shift

The vertical shift $C$ of a cosine - function $y = A\cos(Bx)+C$ is the mid - value between the maximum and minimum values. The mid - value between $4$ and $0$ is $\frac{4 + 0}{2}=2$.

Answer:

$y = 2\cos(2\pi x)+2$