The graph shown in the image resembles a transformed cosine function. Let's analyze the key aspects:

1. Amplitude: The graph oscillates between 2 and -2, indicating the amplitude is 2.
2. Period: The graph completes one full cycle between 0 and 360 degrees, indicating the period is 360 degrees.

The general form of a cosine function is $y = A \cos(Bx)$, where:

• $A$ is the amplitude (which is 2 here).
• The period is given by $\frac{360^\circ}{B}$. Since the period is 360 degrees, $B = 1$, meaning there is no horizontal compression/stretching.

Answer:

The correct equation that matches this graph is $2 \cos(x)$, which corresponds to option A.

Would you like more details or have any questions? Here are some related questions:

1. What is the general form of a trigonometric function and how does each parameter affect the graph?
2. How do you determine the amplitude and period from a trigonometric graph?
3. What is the difference between the graphs of $\cos(x)$ and $\sin(x)$?
4. How does changing the coefficient of $x$ in $\cos(Bx)$ affect the graph?
5. How do horizontal shifts affect the graph of trigonometric functions?

Tip: To quickly identify the function from a trigonometric graph, check the amplitude (maximum/minimum values) and the period (distance for one full cycle).