Final answer:
The domain and range for the functions y = -x + 3 and x = y² + 3, both with the constraint y > 2, are expressed in set builder notation as: the domain for the first function is x < 1, for the second function it is x ≥ 7, and the range for both is y .
Step-by-step explanation:
The given functions are y = -x + 3 with a constraint y > 2, and x = y² + 3 with the same constraint y > 2. To determine the domain and range in set builder notation:
- For y = -x + 3, y > 2, solving for y gives us x < 1. Therefore, the domain for this piece would be x < 1.
- For the second function x = y² + 3, y > 2, since y is squared, all x values will be positive and x will be greater than or equal to y² when y is greater than 2. Therefore, the domain would be x and the range would be y .
Note that the point (1,0) is given, but it does not satisfy the constraint y > 2 and is hence not considered in determining the domain and range. Finally, as the constraint y > 2 applies to both functions, the range for both is the same, y .