To determine whether each relation is a
function, we must apply the
definition of a function:
> A
relation is a
function if and only if
each input (x-value) is paired with
exactly one output (y-value).
In other words,
no x-value can be repeated with different y-values. If an x-value appears more than once with different y-values, it’s
not a function.
Let’s go through each problem one by one.
---
1. Table:
```
x | y
5 | 1
5 | 2
5 | 3
5 | 4
```
- Input `x = 5` maps to
four different outputs: 1, 2, 3, 4.
-
✘ Not a function — one input has multiple outputs.
---
2. Mapping Diagram:
Input → Output
6 → 9
8 → 11
11 → 15
14 → 20
- Each input (6, 8, 11, 14) maps to
only one output.
-
✔ Is a function — no repeated inputs.
---
3. Mapping Diagram:
Input → Output
-5 → 2
-2 → 8
1 → 7
0 → 6
- Each input (-5, -2, 1, 0) maps to
only one output.
-
✔ Is a function — all inputs are unique and map to single outputs.
*(Note: Even though output “7” is mapped from input “1”, and output “6” from “0”, that’s fine — outputs can repeat. Only inputs cannot map to multiple outputs.)*
---
4. Set of Ordered Pairs:
(-9, 4)
(2, 8)
(0, 1)
(6, 5)
(2, 3) ← Here’s the problem!
- Input `x = 2` appears
twice: once with y = 8, once with y = 3.
-
✘ Not a function — same input maps to two different outputs.
---
5. Table:
```
x | 6 8 10 12 14
y | -4 2 6 -4 11
```
- All x-values (6, 8, 10, 12, 14) are
unique.
- Even though y = -4 appears twice (for x=6 and x=12), that’s allowed —
outputs can repeat.
-
✔ Is a function — each input has exactly one output.
---
6. Mapping Diagram:
Input → Output
3 → 2
6 → 4
9 → 6
12 → 2
- Inputs: 3, 6, 9, 12 — all
unique.
- Outputs: 2, 4, 6, 2 — output 2 repeats, but that’s fine.
-
✔ Is a function — no input maps to more than one output.
---
7. Set of Ordered Pairs:
(-11, 14)
(-13, 14)
(3, 12)
(1, 14)
(8, 11)
- Check for repeated x-values:
- x = -11 → y = 14
- x = -13 → y = 14
- x = 3 → y = 12
- x = 1 → y = 14
- x = 8 → y = 11
→ All x-values are
different.
→ Even though y = 14 appears multiple times, that’s okay.
✔ Is a function
---
8. Table:
```
x | y
-9 | 4
-8 | 3
-8 | 1 ← Problem!
-6 | 0
-4 | -3
```
- Input `x = -8` appears
twice, with y = 3 and y = 1.
-
✘ Not a function — same input maps to two different outputs.
---
##
✔ Final Answers:
1.
No
2.
Yes
3.
Yes
4.
No
5.
Yes
6.
Yes
7.
Yes
8.
No
---
## 💡 Key Takeaway:
Remember:
“One input → One output” is the rule for functions. Repeated outputs? Fine. Repeated inputs with different outputs? Not a function.
Let me know if you’d like a visual diagram or further explanation!
Parent Tip: Review the logic above to help your child master the concept of basic functions worksheet.
