In mathematics, **domain** and **range** refer to two essential concepts in relation to functions.

1. **Domain**: The domain of a function is the set of all possible input values (usually the \(x\)-values) for which the function is defined. In other words, it's the complete set of all possible independent variable values that can be plugged into the function.

   Example: For the function \( f(x) = \frac{1}{x-2} \), the domain is all real numbers **except** \( x = 2 \) (since division by zero is undefined). So the domain is \( x \in (-\infty, 2) \cup (2, \infty) \).

2. **Range**: The range of a function is the set of all possible output values (usually the \(y\)-values) that the function can produce. It describes the set of dependent variable values that result from using the function's domain.

   Example: For the function \( f(x) = x^2 \), the range is \( y \geq 0 \), since squaring any real number gives a non-negative result.

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Here are some related questions to explore:

1. What is the domain of a trigonometric function like \( \sin(x) \)?
2. How do you find the domain and range of a composite function?
3. What is the range of a logarithmic function, such as \( \log(x) \)?
4. Can a function have a restricted domain but an infinite range?
5. How do you determine the domain and range of a rational function?

**Tip**: To find the domain of a function, look for values that make the function undefined, such as division by zero or taking the square root of a negative number.

Explore the key concepts of domain and range in functions with examples such as f(x) = 1 / (x - 2) and f(x) = x^2. Learn how to identify the domain and range of different types of functions, including rational and quadratic functions. Suitable for students in Grades 9-12.

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