Identify the domain of the function you’re working with (the set of allowable inputs)
For a given function, list all restrictions on the variable
Exclude values that make the expression invalid, such as:
Denominators equal to 0
Even roots of negative numbers (in real numbers)
Logarithm arguments less than or equal to 0
Square roots of negative numbers
Values that cause tangent/cotangent to be undefined (e.g., where cosine = 0)
Solve the restrictions as inequalities or equations
Combine the results using intersection of all conditions
Write the domain in interval notation or set notation
If the problem states a domain explicitly (e.g., “find the domain of the function” with additional context), use those constraints too
For piecewise functions, take the union of the valid domains from each piece, ensuring the piece conditions are satisfied
For relations (not functions), use the set of all x-values that appear in at least one ordered pair
For graphs, read the x-values where the graph exists (including open/closed circles) and convert to interval notation