https://file.aiquickdraw.com/mathbot/file/1727350905144cymb2c4x.jpg

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.

Observe the graphical representation of two trigonometric functions f(x) and g(x). Identify the correct equations for f(x) and g(x) from the given alternatives.

This problem focuses on identifying sine and reflected sine functions from their graphs. Learn how to determine equations like f(x) = sin(x) and g(x) = -sin(x) based on their graphical characteristics.

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