Question
What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function?
Answers
GPT-4o
For two points, (5, –2) and (x, y), to represent a function, they must satisfy the definition of a function. In the context of a function defined by its domain and range, this means that no two points in the set can have the same first coordinate (x-coordinate) with different second coordinates (y-coordinates).
Given the first point is (5, –2), the first coordinate is 5. For these two points to be part of a function, the second point (x, y) must have a different x-coordinate from 5. Therefore, the possible values for \( x \) are any real numbers except 5.
In summary:
- \( x \neq 5 \)
- \( y \) can be any real number.
These conditions ensure that the relation defined by these points is a function.
Given the first point is (5, –2), the first coordinate is 5. For these two points to be part of a function, the second point (x, y) must have a different x-coordinate from 5. Therefore, the possible values for \( x \) are any real numbers except 5.
In summary:
- \( x \neq 5 \)
- \( y \) can be any real number.
These conditions ensure that the relation defined by these points is a function.