How do I use domain and range in functions?

When you study functions — for instance, those in which y is a function of x — some properties and characteristics are important when you are choosing and using them. Here's an overview of two important properties: domain and range.

 The domain of a function contains all of the possible input values that you can use — every number that can be put into the formula or equation and get a real answer.

The range of a function contains all of the possible output values — every number that is a result of putting input values into the formula or equation.

When determining the domain and range of functions, just a few operations cause restrictions or special attention. Functions with radicals that have even roots will have restricted domains. You can't take the square root or fourth root of a negative number, so any x value that would create that situation has to be eliminated from the domain. Fractions also have to be considered carefully. Any x value that creates a 0 in the denominator has to be eliminated from the domain. Functions with even-powered radicals or absolute value will have restricted ranges. They'll produce just positive results. Other "special" cases will have to be determined by trying a few coordinates or by putting x values into the function equation.