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

Explanation:

Step1: Determine the amplitude A

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

Step2: Determine the period and find B

The standard period of $y = \cos(x)$ is $2\pi$. The period of the given graph is also $2\pi$. Since the period formula is $T=\frac{2\pi}{B}$ and $T = 2\pi$, then $2\pi=\frac{2\pi}{B}$, so $B = 1$.

Step3: Determine the phase - shift C

The graph of $y=\cos(x)$ has a maximum at $x = 0$, and the given cosine - type graph also has a maximum at $x = 0$, so there is no phase - shift, $C = 0$.

Step4: Determine the vertical shift D

The mid - line of the graph is $y = 0$. So, $D=0$.

Answer:

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