what is the equation of the function below? * make sure you have a y= in your equation ex: y=12cos(2pi/3x)+5…

Explanation:

Step1: Determine the amplitude

The amplitude $A$ is half the vertical distance between the maximum and minimum values. The maximum value is 60 and the minimum is - 20. So $A=\frac{60 - (-20)}{2}=\frac{80}{2}=40$.

Step2: Determine the vertical shift

The vertical - shift $D$ is the average of the maximum and minimum values. So $D=\frac{60+( - 20)}{2}=\frac{40}{2}=20$.

Step3: Determine the period

The period $T$ is the horizontal distance between two consecutive maxima. Here, $T = 80$. The formula for the period of a cosine function $y = A\cos(Bx)+D$ is $T=\frac{2\pi}{B}$. Solving for $B$ when $T = 80$, we get $B=\frac{2\pi}{T}=\frac{2\pi}{80}=\frac{\pi}{40}$.

Answer:

$y = 40\cos(\frac{\pi}{40}x)+20$