The given function \( f(x) = 3 \sin x \) is a trigonometric function, where "sen" is the notation for the sine function in some languages. Here is a detailed analysis:

1. **Function Definition:**
   \[
   f(x) = 3 \sin x
   \]

2. **Amplitude:**
   The amplitude of the sine function is the coefficient in front of the sine term. In this case, the amplitude is 3, which means the function will oscillate between -3 and 3.

3. **Period:**
   The period of the sine function is \(2\pi\). Since there is no horizontal stretch or compression factor in the argument of the sine function (i.e., it is just \(x\)), the period remains \(2\pi\).

4. **Phase Shift:**
   There is no phase shift in this function because there is no horizontal translation term added to \(x\).

5. **Vertical Shift:**
   There is no vertical shift in this function since there is no constant term added or subtracted.

6. **Graph:**
   The graph of \(f(x) = 3 \sin x\) will be a sine wave oscillating between -3 and 3, with a period of \(2\pi\).

Would you like any specific details or have any questions about this function?

Here are some questions you might ask next:
1. How do you find the derivative of \( f(x) = 3 \sin x \)?
2. What is the integral of \( f(x) = 3 \sin x \)?
3. How do you find the zeros of \( f(x) = 3 \sin x \)?
4. What is the value of \( f(x) \) at \( x = \pi/2 \)?
5. How do you graph \( f(x) = 3 \sin x \) by hand?

**Tip:** When analyzing trigonometric functions, always check for amplitude, period, phase shift, and vertical shift to fully understand their behavior.

Explore the function f(x) = 3 sen x, a trigonometric function analysis. Learn about its amplitude, period, phase shift, and vertical shift. Detailed insights into trigonometric functions and their properties.

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