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what is the internal notation domain and range ?

To determine the interval notation for the domain and range of the graph in the image, let's break down the analysis:

### 1. **Domain:**
   - **Observation:** The graph extends horizontally in both directions along the x-axis. 
   - **Interpretation:** Since this is likely a trigonometric function, such as a sine or cosine function, which are continuous and periodic, the domain includes all real numbers.
   - **Interval Notation:** The domain is 
     \[
     (-\infty, \infty)
     \]

### 2. **Range:**
   - **Observation:** The graph oscillates between a maximum and minimum value vertically on the y-axis. It appears to reach a maximum value of approximately 2 and a minimum value of approximately -2.
   - **Interpretation:** The range of the function is the set of all y-values that the graph attains.
   - **Interval Notation:** The range is 
     \[
     [-2, 2]
     \]

So, the interval notation for the domain and range of the graph is:

- **Domain:** \((- \infty, \infty)\)
- **Range:** \([-2, 2]\)

Would you like more details or have any questions?

### Related Questions:
1. How do you determine the domain of a trigonometric function?
2. What are the typical ranges for sine and cosine functions?
3. How can phase shift affect the domain and range of a function?
4. What transformations can change the range of a trigonometric function?
5. How do vertical and horizontal shifts impact the graph of a trigonometric function?
6. Can the range of a sine or cosine function be altered by changing the amplitude?
7. How does the period of a function relate to its domain?
8. What is the significance of symmetry in determining the range of trigonometric functions?

**Tip:** When analyzing trigonometric functions, always start by identifying the amplitude, period, and any shifts in the function, as these will directly influence the domain and range.

Explore how to determine the interval notation for the domain and range of trigonometric functions. Learn about the continuous and periodic nature of trigonometric graphs, and how to interpret and express their domain and range using interval notation. Suitable for high school students and anyone studying trigonometry.

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