Let's go through each of the 8 problems and determine whether each
relation is a
function.
---
🔹 Definition: What is a Function?
A
function is a relation where
each input (x-value) has
exactly one output (y-value).
In other words:
- No x-value can be paired with more than one y-value.
- If any x-value appears more than once with different y-values, it’s
not a function.
We’ll apply this rule to each problem.
---
✔ Problem 1:
| x | y |
|---|---|
| 5 | 1 |
| 5 | 2 |
| 5 | 3 |
| 5 | 4 |
- The
same input (x = 5) maps to
multiple outputs (1, 2, 3, 4).
-
✘ Not a function
>
Answer: Not a function
---
✔ Problem 2:
Input → Output:
- 6 → 9
- 8 → 11
- 11 → 15
- 14 → 20
Each input maps to
only one output.
- All inputs are unique and have only one arrow.
- ✔️
Yes, it's a function
>
Answer: Yes, it's a function
---
✔ Problem 3:
Input → Output:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6
Wait — look closely:
- Input
1 maps to
both 7 and 6?
- From the diagram: 1 has arrows to both 7 and 6?
✔ Wait — let's double-check:
- Arrow from 1 → 7
- Arrow from 1 → 6? Is that correct?
Looking at the diagram:
- Yes,
input 1 points to
both 7 and 6 → two outputs for one input.
-
✘ Not a function
>
Answer: Not a function
---
✔ Problem 4:
Ordered pairs:
- (-9, 4)
- (2, 8)
- (0, 1)
- (6, 5)
- (2, 3)
Look at
x = 2: it appears twice:
- (2, 8) and (2, 3) → same input, different outputs
-
✘ Not a function
>
Answer: Not a function
---
✔ Problem 5:
| x | y |
|---|---|
| 6 | -4 |
| 8 | 2 |
| 10 | 6 |
| 12 | -4 |
| 14 | 11 |
Check if any x-value repeats:
- All x-values are different: 6, 8, 10, 12, 14 → all unique
- Each x maps to exactly one y
- ✔️
Yes, it's a function
>
Answer: Yes, it's a function
---
✔ Problem 6:
Input → Output:
- 3 → 2
- 6 → 4
- 9 → 6
- 12 → 2
Check each input:
- 3 → 2
- 6 → 4
- 9 → 6
- 12 → 2
All inputs are unique and map to only one output.
Even though
2 appears as output twice, that’s fine —
outputs can repeat, but
inputs cannot.
✔️
Yes, it's a function
>
Answer: Yes, it's a function
---
✔ Problem 7:
Ordered pairs:
- (-11, 14)
- (-13, 14)
- (3, 12)
- (1, 14)
- (8, 11)
Check x-values:
- -11, -13, 3, 1, 8 → all
unique
- No repeated x-values
- ✔️
Yes, it's a function
>
Answer: Yes, it's a function
---
✔ Problem 8:
| x | y |
|---|---|
| -9 | 4 |
| -8 | 3 |
| -8 | 1 |
| -6 | 0 |
| -4 | -3 |
Look at
x = -8: appears
twice
- Once with y = 3
- Once with y = 1 → same input, different outputs
-
✘ Not a function
>
Answer: Not a function
---
✔ Final Answers Summary:
| Problem | Is it a function? | Reason |
|--------|-------------------|--------|
| 1 |
✘ No | x = 5 maps to multiple y-values |
| 2 |
✔ Yes | Each input has one output |
| 3 |
✘ No | x = 1 maps to both 6 and 7 |
| 4 |
✘ No | x = 2 maps to both 8 and 3 |
| 5 |
✔ Yes | All x-values unique |
| 6 |
✔ Yes | All inputs unique |
| 7 |
✔ Yes | All x-values unique |
| 8 |
✘ No | x = -8 maps to two different y-values |
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✔ Final Answer Key:
1.
No
2.
Yes
3.
No
4.
No
5.
Yes
6.
Yes
7.
Yes
8.
No
Let me know if you'd like this in a printable format or need explanations drawn on the image!
Parent Tip: Review the logic above to help your child master the concept of functions math worksheet.
