Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

Grade 10 › C10U07 Linear Relations & Functions › L2
GRADE 10 · ALBERTAOUTCOME RF2

L2 · Relations and Functions: What Makes It a Function

Learning goal

“I can decide whether a relation is a function - from ordered pairs, a table, a mapping diagram, or a graph described in words - and explain the rule I used.”

Function — a relation in which each input has exactly ONE output.
Mapping diagram — two lists (inputs, outputs) with arrows showing which input pairs with which output.
Vertical line test — a graph represents a function if every vertical line crosses it at most once.
Input / output — the first coordinate of an ordered pair is the input; the second is the output. (Formal names - independent/dependent variable - arrive in L5.)
Worked example

Relation A: {(1, 3), (2, 5), (3, 5), (4, 7)}. Check each input: 1 -> 3, 2 -> 5, 3 -> 5, 4 -> 7. No input repeats, so each input has exactly one output: A IS a function. Notice 5 appears as an output twice - that is allowed; the rule restricts inputs, not outputs. Relation B: {(2, 1), (2, 4), (3, 5)}. Input 2 has two outputs (1 and 4) - B is NOT a function. Say it plainly: every function is a relation, but a relation is a function only when no input is paired with more than one output.

Check yourself — explain it

{(1, 4), (2, 4), (3, 4)} is a function because...

Paired problem — example still visible

Is {(0, 1), (1, 1), (2, 3), (3, 3)} a function? -> Yes - inputs 0, 1, 2, 3 each appear once.

Faded completion — last step is yours

"In {(5, 2), (6, 2), (__, 9), (7, 9)}, the missing input that would BREAK the function property is ___." -> 5, 6 or 7 (any input already present); e.g. 5 - it would give input 5 two outputs, 2 and 9

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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