For the function \( y = \sin(2x) \), the **domain** and **range** can be determined as follows:

### **Domain:**
- The sine function, \( \sin(x) \), is defined for all real numbers \( x \). Therefore, the domain of \( y = \sin(2x) \) is also all real numbers.
  
  \[
  \text{Domain} = (-\infty, \infty)
  \]

### **Range:**
- The range of the sine function is the set of all possible output values. Since \( \sin(2x) \) oscillates between -1 and 1, the range of \( y = \sin(2x) \) is:
  
  \[
  \text{Range} = [-1, 1]
  \]

Would you like to explore other aspects of this function or need further explanations?

### Related Questions:
1. What are the maximum and minimum values of \( y = \sin(2x) \)?
2. How does the frequency affect the domain and range of \( y = \sin(2x) \)?
3. What is the effect of a vertical shift on the range of \( y = \sin(2x) \)?
4. How does the function \( y = \sin(2x) \) behave as \( x \) approaches infinity?
5. Can the domain of \( y = \sin(2x) \) ever be restricted, and what would that look like?

### Tip:
When dealing with trigonometric functions, remember that the domain is typically all real numbers, but the range is constrained by the nature of the function's oscillation.

Understand the domain and range of the function y = sin(2x) with a detailed explanation. Explore how the sine function's properties affect the domain (-∞, ∞) and the range [-1, 1]. Suitable for high school students studying trigonometry and functions.

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