find an equation for the cosine graph, f(x):\nwrite your answer in the form f(x) = a cos(bx + c) + d, where…

Explanation:

Step1: Find the amplitude A

The amplitude is half the vertical distance between the maximum and minimum values. The maximum value is 6 and the minimum is 4. So, $A=\frac{6 - 4}{2}=1$.

Step2: Find the vertical - shift D

The vertical - shift is the average of the maximum and minimum values. So, $D=\frac{6 + 4}{2}=5$.

Step3: Find the period and B

The period of the cosine function is the distance between two consecutive peaks. From the graph, the period $T = 2\pi$. Since the formula for the period of $y = A\cos(Bx + C)+D$ is $T=\frac{2\pi}{B}$, and $T = 2\pi$, then $B = 1$.

Step4: Find the phase - shift C

The graph has no horizontal shift, so $C = 0$.

Answer:

$f(x)=1\cos(1x + 0)+5=\cos(x)+5$