Given the relation: [tex]\((-4, 16), (0, 0), (2, 4), (4, 16)\)[/tex], let's address each part of the question systematically.
### (a) State the domain
The domain of a relation is the set of all the first elements (x-values) in each ordered pair.
Given the ordered pairs [tex]\((-4, 16), (0, 0), (2, 4), (4, 16)\)[/tex], the x-values are:
- -4
- 0
- 2
- 4
Therefore, the domain is [tex]\((-4, 0, 2, 4)\)[/tex].
### (b) State the range
The range of a relation is the set of all the second elements (y-values) in each ordered pair.
Given the ordered pairs [tex]\((-4, 16), (0, 0), (2, 4), (4, 16)\)[/tex], the y-values are:
- 16
- 0
- 4
- 16
Note that [tex]\(16\)[/tex] appears twice, but since we list each value once in the range, we get the values:
- 16
- 0
- 4
Therefore, the range is [tex]\((16, 0, 4)\)[/tex].
### (c) State if the relation is a function and why or why not
A relation is a function if each x-value in the domain is associated with exactly one y-value in the range. This means that all x-values (the domain) must be unique.
Given the domain from part (a) [tex]\((-4, 0, 2, 4)\)[/tex], each x-value is unique (i.e., no x-value repeats). This satisfies the condition for the relation to be a function.
Therefore, the relation is a function because all the x-values are unique.
### Conclusion
Given the information:
(a) The domain is [tex]\((-4, 0, 2, 4)\)[/tex].
(b) The range is [tex]\((16, 0, 4)\)[/tex].
(c) Yes, the relation is a function because all the x-values are unique.
So, the correct answer is:
OA) (a) [tex]\((-4, 0, 2, 4)\)[/tex], (b) [tex]\((16, 0, 4)\)[/tex], (c) Yes, the relation is a function because all the x-values are unique.
