To determine whether each mapping diagram represents a
function, we use the
definition of a function:
> A
function is a relation where
each input (element in the domain) is associated with
exactly one output (element in the range).
> That means:
> - Every element in the domain must have
at least one arrow (mapped to something).
> - No element in the domain can have
more than one arrow pointing to different outputs.
Let’s go through each diagram one by one.
---
1)
- Domain: {0, 1, 2, 5, 6}
- Each element has exactly
one arrow.
- No element maps to more than one value.
✔ Function
---
2)
- Domain: {2, 3, 4, 6, 9}
- Check each:
- 2 → 0
- 3 → 4
- 4 → 6
- 6 → 0 and 6? Wait — 6 points to
both 0 and 6 → two outputs!
✘ Not a Function
>
Reason: Element
6 maps to
two different values (0 and 6), so it violates the "one output per input" rule.
---
3)
- Domain: {2, 8, 9}
- All elements map to
only one value.
- But notice: all three map to
5 — that's allowed! Multiple inputs can map to same output.
✔ Function
---
4)
- Domain: {0, 1, 4, 9}
- Check:
- 0 → 2 and 8? Wait — 0 has arrows to
2 and 8 → two outputs!
✘ Not a Function
>
Reason: 0 maps to both 2 and 8 → not allowed.
---
5)
- Domain: {1, 2, 4, 5, 9}
- Each element has
exactly one arrow.
- Even though multiple inputs map to same outputs (e.g., 2 and 5 both go to 7), that's okay.
✔ Function
---
6)
- Domain: {0, 6, 8}
- All three elements map to
6.
- Each has only one arrow.
✔ Function
> Allowed: multiple inputs can map to same output.
---
7)
- Domain: {1, 2, 8}
- Each element has exactly one arrow.
- 1 → 4
- 2 → 5
- 8 → 9
✔ Function
---
8)
- Domain: {0, 2, 4, 7}
- Check:
- 0 → 3
- 2 → 6
- 4 → 9
- 7 → 6 and 9? Wait — 7 has arrows to
both 6 and 9!
✘ Not a Function
>
Reason: 7 maps to two outputs → violates function rule.
---
✔ Final Answers:
| Number | Answer |
|--------|--------------|
| 1) |
Function |
| 2) |
Not Function |
| 3) |
Function |
| 4) |
Not Function |
| 5) |
Function |
| 6) |
Function |
| 7) |
Function |
| 8) |
Not Function |
---
🔍 Summary Rule:
- A mapping is a
function if
every domain element has exactly one arrow (no more, no less).
- If any domain element has
two or more arrows, it's
not a function.
- It's okay for
multiple domain elements to point to the
same range element.
Let me know if you'd like this formatted for printing or need explanations in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of relations and functions worksheet pdf.
