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.

Would you like details or have any questions?

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.