Identify the input variable and determine all values it can take without causing undefined expressions
Exclude values that make denominators equal to zero
Exclude values that make even roots have negative radicands
Exclude values that make logarithms have nonpositive arguments
Consider any restrictions from piecewise definitions
Combine all valid input values to get the domain
Determine the output values the function can produce
Analyze the function’s algebraic form, graph, or transformations
Solve for the output variable when possible to find allowable values
Check for maximum and minimum values if the function is bounded
Consider asymptotes, holes, and discontinuities
Use the graph to identify all y-values attained by the function
Write the set of all possible outputs to get the range