write the equation of the trigonometric funct...

# Explanation: ## Step1: Determine the amplitude The maximum value is 5 and the minimum is 1. Amplitude $A=\frac{5 - 1}{2}=2$. ## Step2: Determine the vertical shift The mid - line is $y=\frac{5 + 1}{2}=3$, so $D = 3$. ## Step3: Determine the period The period $T=2\pi$. Since $T=\frac{2\pi}{B}$ and $T = 2\pi$, then $B = 1$. ## Step4: Determine the phase shift The graph starts at its maximum, which is a cosine - type graph with no phase shift, so $C=0$. The general form of a cosine function is $y=A\cos(Bx - C)+D$. # Answer: $y = 2\cos(x)+3$