g10-05-01 · Core topics
Repair one mapping arrow
Can two inputs share an output? Which single input breaks the function rule?
1 MIN · PREDICT ON PAPER
Before changing the diagram, mark each input with 0, 1 or 2 distinct outputs.
Discuss or write first. No typed answer is required to continue.
A = {1, 2, 3}; B = {5, 7}; attained range = {5, 7}.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
A function gives every allowed input exactly one output. Many-to-one is permitted; a missing arrow or two different outputs from one input violates the rule.
Conditions: The input set is {1,2,3}. Count distinct outputs from each input, not arrows arriving at an output.
Mathematical justification: Check the defining statement for each of the three inputs. This exhausts this finite mapping; it does not prove a claim about every possible mapping.
1 MIN · EXIT CHECK
All three inputs map to 8. Function or not, and why?
Check after answering
Yes: each input has exactly one output.
Teacher guidance and extension
Before: Read function inputs, outputs and the stated domain; write your first prediction on paper.
Ask: Ask a student to repair the missing-arrow case, then ask another to justify allowing shared output 5.
Watch for: Different inputs must have different outputs.
Challenge: Make every input map to 8. Explain why unused elements of the output set are harmless.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
Paper responses are enough. Drafts remain in this tab; choose local saving to include them in the existing complete backup.
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