Domain & Range

Domain of a function is the largest possible set of input to make the function defined. The range is the interval of the function value where the function is defined. If the function is y = f (x), the biggest set of x values is the domain and the interval of y values is the range; if the function is z = f (x,y), the biggest combination set of x and y values is the domain and the interval of the output, z values, is the range. 

The graphs below give some examples for better understanding. Please just choose one function at a time to avoid overlapping of domain and/or range of the functions.

A) Function of one variable

The line in purple on the x-axis indicate the interval of the domain, whereas the red line on y-axis indicate the interval of the range. Take note of the domain and range stated in the upper box so that you know how to write it by yourself.

B) Functions of several variables

The graph of the domain is shown at the lower left box and the graph of the function is shown at the right. The interval of the range is marked in the graph at right with light green line. Please click here if you want to have better viewing experience for 3D graphs. Take note of the domain and range stated in the upper box, it is slightly different with the writing of domain as in part A) since the functions involved are functions of more than one variable.

Betty, created with GeoGebra and Thomas' Calculus, Pearson.