The question asks to identify the correct functions for $f(x)$ and $g(x)$ based on their graphical representations.

1. The green curve labeled as $f(x)$ resembles the sine function $\sin(x)$, as it starts from zero, increases to a maximum of 1 at $\frac{\pi}{2}$, and decreases to zero at $\pi$.

2. The red curve labeled as $g(x)$ appears to be a reflection of the sine function across the x-axis. This matches $-\sin(x)$, as the function starts from zero, decreases to a minimum of -1 at $\frac{\pi}{2}$, and returns to zero at $\pi$.

Thus, the two correct alternatives are:

• $f(x) = \sin(x)$
• $g(x) = -\sin(x)$

Let me know if you'd like more details! Here are five related questions you can explore:

1. How is the amplitude of a sine or cosine function modified?
2. What transformations result in a vertical reflection of a function?
3. How would the graph of $f(x) = 2\sin(x)$ differ from $f(x) = \sin(x)$?
4. Can you express $\cos(x)$ in terms of a phase shift of $\sin(x)$?
5. What is the period of $\sin(x)$ and how does it affect its graph?

Tip: Remember that multiplying a function by $-1$ reflects it across the x-axis.