Question

2. In order for the relation below to be a function, which value is not allowed to be the missing x-value?
{(2, 8), (4, 5), (7, 3), (9, 0), (?, 6)}
A) 3
B) 0
C) 1
D) 7

3. Match each domain in the first column to the equivalent interval notation domain in the second column.
4 < x ≤ 8
4 ≤ x < 8
4 < x < 8

A) (4, 8)
B) [4, 8]
C) (4, 8]
D) [4, 8)

Answer 1

### For the first question (Question 2):
A relation is a function if every x-value is associated with exactly one y-value. In the given relation:

\[
\{(2, 8), (4, 5), (7, 3), (9, 0), (?, 6)\}
\]

the only x-value already present is 2, 4, 7, and 9. The missing x-value cannot be any of these values to maintain its status as a function.

Therefore, if the missing x-value is:
- A) 3 - Allowed (since it is not in the set)
- B) 0 - Allowed (since it is not in the set)
- C) 1 - Allowed (since it is not in the set)
- D) 7 - Not Allowed (since 7 is already mapped to a y-value of 3)

Thus, the value that is **not allowed** for the missing x-value is **D) 7**.

### For the second question (Question 3):
Looking at the domains and their corresponding interval notation:

1. **4 < x ≤ 8** corresponds to **(4, 8]** - it does not include 4 but includes 8.
2. **4 ≤ x < 8** corresponds to **[4, 8)** - it includes 4 but does not include 8.
3. **4 < x < 8** corresponds to **(4, 8)** - it does not include 4 and does not include 8.

Thus, the matches are:
- **4 < x ≤ 8** → **C) (4, 8]**
- **4 ≤ x < 8** → **D) [4, 8)**
- **4 < x < 8** → **A) (4, 8)**

So the interval notation matches are:
- 4 < x ≤ 8 → C) (4, 8]
- 4 ≤ x < 8 → D) [4, 8)
- 4 < x < 8 → A) (4, 8)