2. In order for the relation below to be a function, which value is not allowed to be the missing x-value?

Question

{(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)