To determine the domain and range of the function given by the set of points [tex]\(\{(-3,4),(-1,7),(5,9)\}\)[/tex], we need to consider the x-coordinates and y-coordinates separately.
1. Domain:
The domain of a function is the set of all possible input values (x-coordinates) for which the function is defined.
- From the point [tex]\((-3, 4)\)[/tex], the x-coordinate is [tex]\(-3\)[/tex].
- From the point [tex]\((-1, 7)\)[/tex], the x-coordinate is [tex]\(-1\)[/tex].
- From the point [tex]\((5, 9)\)[/tex], the x-coordinate is [tex]\(5\)[/tex].
Therefore, the domain of the function is [tex]\([-3, -1, 5]\)[/tex].
2. Range:
The range of a function is the set of all possible output values (y-coordinates) that the function can take.
- From the point [tex]\((-3, 4)\)[/tex], the y-coordinate is [tex]\(4\)[/tex].
- From the point [tex]\((-1, 7)\)[/tex], the y-coordinate is [tex]\(7\)[/tex].
- From the point [tex]\((5, 9)\)[/tex], the y-coordinate is [tex]\(9\)[/tex].
Therefore, the range of the function is [tex]\([4, 7, 9]\)[/tex].
In summary, for the function given by the set of points [tex]\(\{(-3, 4), (-1, 7), (5, 9)\}\)[/tex]:
- The domain is [tex]\([-3, -1, 5]\)[/tex].
- The range is [tex]\([4, 7, 9]\)[/tex].
