A Function Sends Each Input to Exactly One Output
A function is a correspondence that gives every input one output and only one. That single condition decides whether a rule is a function at all, which constant makes it one, and how many functions exist between two finite sets (multiply the allowed choices for each input). Running the rule backwards recovers every input that lands on a given output.
grade 7–8 Functions Make a Systematic ListEliminate Possibilities
Progression (4)
g7 1. Run a counting rule backward to every input ExpressionsOperations
g8 2. Two equal inputs break a function FunctionsExpressions
g8 3. Exactly one prime sum makes a function FunctionsOperations
g8 4. Count functions by multiplying output choices FunctionsData & probability