Question

5 which relation below is not a function?
a
domain
-2
-1
0
1
2
range
2
0
2
5
b
domain
-2
-1
0
1
2
range
-2
-2
0
3
3
c
domain
-2
-1
0
1
2
range
5
5
5
5
5
d
domain
-2
-1
0
1
2
range
5
6
6
7
8

Explanation:

To determine if a relation is a function, we use the definition: a function is a relation where each element in the domain is paired with exactly one element in the range. Let's analyze each option:

• Option A: The domain element \( 0 \) is paired with two range elements (\( 0 \) and \( 2 \)). This violates the definition of a function because one domain element maps to multiple range elements.
• Option B: Each domain element (\( -2, -1, 0, 1, 2 \)) is paired with exactly one range element. Multiple domain elements can map to the same range element (e.g., \( -2 \) and \( -1 \) both map to \( -2 \)), which is allowed in a function.
• Option C: Each domain element maps to the single range element \( 5 \). This is a valid function (a constant function).
• Option D: Each domain element is paired with exactly one range element. Overlapping arrows (e.g., \( -2 \) and \( -1 \) mapping to \( 5 \) and \( 6 \)) do not violate the function definition as long as each domain element has one range pair.

Answer:

A. Domain and Range mapping where 0 in Domain maps to 0 and 2 in Range