## Domain and Range 1: Basic Concepts

Domain and range are concepts that are essential in learning functions.  In most resources, these concepts are just defined technically, and although there are examples, many just lack intuitive explanations. In this post, we discuss domain and range in a simple and hopefully easy to understand manner.

Example 1: $f(x) = 2x + 1$

Domain

What is the domain of $f(x) = 2x + 1$ and what is its range? Well, the domain are just the possible values of $x$ that will produce a “valid” value $f(x)$. To check, we can ask the following questions.

• Can we substitute positive values to $x$?
• Can we substitute negative values to $x$?
• Can we substitute 0 to $x$?

Obviously, the answer to these questions are all yes. In fact, we can assign any real number value to $x$ and we can always get a corresponding value for $f(x)$. » Read more