Chapter 3 · Functions
Check that every allowed input has exactly one output; distinguish many-to-one from one-to-many.
Drag a handle or select an object, then tap its destination.
Give your reason before checking.
| Input | Distinct outputs | Count |
|---|---|---|
| 1 | {5} | 1 |
| 2 | {5} | 1 |
| 3 | {7} | 1 |
Tab to an object. Arrow keys move handles; Enter selects a card or places it at a destination.
Select an object
Select a destination
Works stay in this open page. Use the common notebook for consent-based saved notes.
Chapter 3 · Functions
Class ______ Name __________________ Date __________
Before changing the arrows, mark every input that has no output or two different outputs. Predict whether two inputs may share an output.
Draw A = {1, 2, 3}, B = {5, 7} with 1 → 5, 2 → 5, 3 → 7. Record the number of outputs for each input.
Remove the arrow from 3; then restore it and add 2 → 7. For each version, identify the input that breaks the function condition and one repair.
For A = {1, 2, 3}, B = {6, 8, 10}, send all inputs to 8. Record the domain, the output set B and the attained range separately.
Students are matched to their birth month, and birth months to students. Which direction always defines a function when every student has one recorded birth month? Explain the direction of the input.
A = {a, b, c}, B = {1, 2}. The arrows are a → 1, b → 1, c → 1 and c → 2. Is this a function? Give one smallest repair.
Chapter 3 · Functions · Teacher reference
3.1.1(第1課時) · 01_從對應認識函數.docx
5 min predict the faulty inputs; 12 min repair arrows; 8 min state the definition; 12 min paper examples; 3 min exit check.
Before changing the arrows, mark every input that has no output or two different outputs. Predict whether two inputs may share an output.
A function assigns exactly one output to every element of its domain. Sharing an output is allowed, so the first and constant-output diagrams are functions. An unused element of B does not invalidate a function. The actual range contains only outputs reached by an arrow; in the constant example it is {8}.
Students are matched to their birth month, and birth months to students. Which direction always defines a function when every student has one recorded birth month? Explain the direction of the input.
A = {a, b, c}, B = {1, 2}. The arrows are a → 1, b → 1, c → 1 and c → 2. Is this a function? Give one smallest repair.
No: c has two distinct outputs. Remove either c → 1 or c → 2; one arrow removal is enough.
