Identify all input values allowed for the function
Exclude values that make the denominator zero
Exclude values that make an even root negative
Exclude values that make a logarithm undefined
Consider any restrictions from piecewise definitions
Use the graph to see which x-values are included for the domain
Write the domain in interval notation or set notation
Determine all possible output values of the function
Use the graph to see which y-values are included for the range
Check for maximum and minimum values
Check for asymptotes and gaps
Consider whether outputs are restricted by roots, fractions, or logs
Write the range in interval notation or set notation