To find the domain and range of a function, it depends on what kind of function you're referring to. In general terms:

- **Domain** refers to the set of all possible input values (x-values) for which the function is defined.
- **Range** refers to the set of all possible output values (y-values) that the function can produce based on the domain.

Here’s how you approach finding them:

### 1. **Domain:**
   - Look for any restrictions on the input. These often include:
     - Denominators that cannot be zero (for rational functions).
     - Radicals (square roots, cube roots, etc.) where the expression inside must be non-negative for even roots.
     - Logarithmic functions, where the argument must be positive.
   - If there are no restrictions, the domain is usually all real numbers \( (-\infty, \infty) \).

### 2. **Range:**
   - This depends on the nature of the function. You analyze the behavior of the function to determine what output values (y-values) can be achieved.
   - For simpler functions (like linear functions), the range is often all real numbers. For more complex functions (like quadratics, trigonometric functions, or logarithmic functions), you’ll need to consider the shape or behavior of the function (e.g., whether it has a minimum or maximum, asymptotes, etc.).

Could you provide a specific function or graph? That way, I can help find the exact domain and range of it.

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Do you want more details or have any questions?

Here are some related questions:
1. What is the domain of \( f(x) = \frac{1}{x-2} \)?
2. How do you find the range of a quadratic function?
3. What is the domain of \( f(x) = \ln(x) \)?
4. How does the behavior of asymptotes affect the range?
5. What’s the range of the sine and cosine functions?

**Tip:** Always consider the context and type of function when determining domain and range—some functions have specific rules or restrictions.

Explore how to find the domain and range of functions, including rational and logarithmic functions. Learn about restrictions on input values and how the behavior of a function determines its range. Suitable for high school students (Grades 9-12).

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