From the graph provided, we can determine the function $f(x)$. Here are the characteristics of the function based on the graph:

1. The function has a sinusoidal shape, indicating it is likely a sine or cosine function.
2. The amplitude is $2$, as the graph oscillates between $-2$ and $2$.
3. The period is $360^\circ$, as the graph completes one full cycle between $0^\circ$ and $360^\circ$.
4. The graph starts at $(0, 0)$ and moves upwards, resembling the sine function.

The general form of a sine function is: $f(x) = A \sin(Bx + C) + D$ where:

• $A$ is the amplitude,
• $B$ determines the period ($\text{Period} = \frac{360^\circ}{B}$),
• $C$ is the phase shift,
• $D$ is the vertical shift.

Using the observations:

• Amplitude $A = 2$,
• Period $= 360^\circ$, so $B = 1$,
• No vertical shift, so $D = 0$,
• No phase shift ($C = 0$).

Thus, the equation is: $f(x) = 2 \sin(x)$

Would you like a step-by-step derivation of this or details on related transformations? Here are some questions to explore further:

1. How can we derive the equation if the phase or vertical shift changes?
2. What if the period changes to $180^\circ$ or $720^\circ$? How does that affect $B$?
3. How would the equation differ if it were a cosine function instead of sine?
4. How can you verify sinusoidal equations using transformations of the unit circle?
5. What is the impact of adding a constant $D$ to the function?

Tip: Always identify the amplitude, period, and phase shift when analyzing sinusoidal graphs to determine the function.