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

Explanation:

Step1: Determine the amplitude A

The amplitude is half the 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 B

The period $T$ of the cosine - wave is $2\pi$. 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 $B = 1$.

Step3: Determine the phase - shift C

The graph is not shifted horizontally, so $C = 0$.

Step4: Determine the vertical - shift D

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

Answer:

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