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 2 and the minimum is - 2. So, $A=\frac{2 - (-2)}{2}=2$.

Step2: Find the vertical shift D

The vertical - shift is the mid - value between the maximum and minimum values. So, $D=\frac{2+( - 2)}{2}=0$.

Step3: Find the period and B

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

Step4: Find the phase shift C

The graph of $y = \cos x$ has a maximum at $x = 0$. The given graph also has a maximum at $x = 0$, so the phase shift $C = 0$.

Answer:

$f(x)=2\cos(x)$