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: 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, $A=\frac{2 - (-2)}{2}=\frac{4}{2}=2$.

Step2: Find the period P and B

The period of a cosine - function is the horizontal distance between two consecutive maximums or minimums. Here, the period $P = 2\pi$. The formula for the period of $y = A\cos(Bx + C)+D$ is $P=\frac{2\pi}{|B|}$. Since $P = 2\pi$, then $\frac{2\pi}{|B|}=2\pi$, so $|B| = 1$. We can take $B = 1$ (assuming no horizontal compression or stretch other than the standard).

Step3: Find the phase - shift C

The standard cosine function $y=\cos(x)$ has a maximum at $x = 0$. Our function also has a maximum at $x = 0$, so the phase - shift $C = 0$.

Step4: Find the vertical shift D

The mid - line of the function is the average of the maximum and minimum values. The mid - line is $y=\frac{2+( - 2)}{2}=0$, so $D = 0$.

Answer:

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