To determine which of the given relations is a function, we need to understand the definition of a function. A relation is a function if each input (or domain) corresponds to exactly one output (or range).
Let's analyze each relation:
a. [tex]\(\{(3, -3), (9, -6), (0, -9)\}\)[/tex]
For this relation, we can list the pairs:
- Input 3 maps to output -3.
- Input 9 maps to output -6.
- Input 0 maps to output -9.
Each input has a unique output, so this relation is a function.
b. [tex]\(\{(3, -3), (9, -6), (3, -9)\}\)[/tex]
For this relation:
- Input 3 maps to output -3.
- Input 9 maps to output -6.
- Input 3 also maps to output -9.
Here, the input 3 maps to two different outputs (-3 and -9), so this relation is not a function.
c. [tex]\(\{(3, -3), (9, -6), (9, 2), (0, -9)\}\)[/tex]
For this relation:
- Input 3 maps to output -3.
- Input 9 maps to output -6.
- Input 9 also maps to output 2.
- Input 0 maps to output -9.
Here, the input 9 maps to two different outputs (-6 and 2), so this relation is not a function.
d. [tex]\(\{3, 9, 0, -4\}\)[/tex]
For this relation, there are no pairs of inputs and outputs, just a list of numbers. This does not fit the definition of a function because it lacks the structure of pairs of values representing the domain and range.
Hence, upon examining each relation, we conclude that the given relation that is a function is:
A
So, the best answer is A.
