Identify the input variable and the output variable
Set restrictions on the input values to avoid undefined expressions
Exclude values that make denominators equal to zero
Exclude values inside even roots that would be negative
Exclude values inside logarithms that are zero or negative
Check for any other function-specific restrictions
Write all allowed input values as the domain
Determine the possible output values by analyzing the function
Use algebraic manipulation, graphs, or tables to find output restrictions
Look for maximum and minimum values if the function has them
Check for asymptotes, holes, and endpoints
Write all possible output values as the range
Use interval notation or set notation to express the domain and range