Identify the type of relation: equation, graph, table, or set of ordered pairs
Domain (all possible input values, usually x):
If given a graph: list all x-values where the graph exists (include endpoints if filled; exclude if open)
If given a table: collect all x-values from the ordered pairs
If given ordered pairs: collect all first coordinates (x-values)
If given an equation: solve restrictions from denominators and even roots
Exclude x-values that make any denominator equal to 0
Exclude x-values that make any even root’s radicand negative
Exclude x-values that make logarithm arguments ≤ 0
Range (all possible output values, usually y):
If given a graph: list all y-values the graph attains (include endpoints if filled; exclude if open)
If given a table: collect all y-values from the ordered pairs
If given ordered pairs: collect all second coordinates (y-values)
If given an equation: solve restrictions from denominators and even roots (in terms of y when needed)
Write domain and range in correct notation:
Use interval notation: (a, b), [a, b], (a, b], [a, b)
Use unions for multiple intervals: (-∞, 3) ∪ [5, ∞)
Use set-builder notation if required: {x | condition} and {y | condition}