## Understanding Domain and Range Part 2

In the **previous post**, we have learned the graphical representation of domain and range. The domain of the function is the shadow or projection of the graph of to the x-axis (see the red segment in the figure below). The range of is the projection of the graph of to the y-axis (see the green segment in the figure below). In this post, we are going to learn how to analyze equations of **functions** and determine their domain and range without graphing.

If a graph of a function is projected to the x-axis, the projection is the set of x-coordinates of the graph. A single point on the projection means a point on the graph exists. The existence of a point implies that exists. This means that the function is defined at . In effect, the domain of a function is the set of x-coordinates that makes the function defined. In what follows, we learn some examples to illustrate this concept. » Read more