Question

find an equation for the cosine graph, f(x):

Explanation:

Step1: Recall the general form of cosine function

The general form of a cosine function is \( f(x)=A\cos(Bx - C)+D \).

Step2: Determine the amplitude \( A \)

The amplitude \( A=\frac{\text{Maximum}-\text{Minimum}}{2} \). Here, maximum \( = 1 \), minimum \(=-1 \). So \( A=\frac{1 - (-1)}{2}=1 \).

Step3: Determine the period \( T \) and \( B \)

The period \( T = 2\pi \). Since \( T=\frac{2\pi}{|B|} \), and \( T = 2\pi \), then \( B = 1 \).

Step4: Determine the phase - shift \( C \)

There is no phase - shift, so \( C = 0 \).

Step5: Determine the vertical shift \( D \)

The mid - line \( D=\frac{\text{Maximum}+\text{Minimum}}{2}=\frac{1+( - 1)}{2}=0 \).

Answer:

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