Domain: all possible input values of a function
Range: all possible output values of a function
To find the domain:
Look for values that make the function undefined
Exclude values that make a denominator equal to 0
Exclude values inside an even root that are negative
Exclude values that make a logarithm zero or negative
Use the remaining input values as the domain
To find the range:
Determine all possible output values
Solve the function for the output variable if needed
Check how the graph behaves
Identify minimum and maximum values if they exist
Consider restrictions from roots, fractions, and transformations
Write the set of all possible outputs as the range