Final answer:
The domain and range of a function depend on its definition. Generally, the domain includes all real numbers unless there are specific restrictions, and the range includes all possible outputs of the function. The statements regarding the domain and range of f(x), g(x), and h(x) are based on typical characteristics of functions and require additional information to confirm.
Step-by-step explanation:
The student has presented functions f(x), g(x), and h(x) with a partial description and asks for the domain and range of these functions. Although the full definition of these functions is not provided, certain general statements can be made regarding domains and ranges of functions:
- A domain of a function consists of all the values for which the function is defined, typically all real numbers unless there are restrictions such as division by zero or square roots of negative numbers.
- A range of a function is the set of all possible outputs of the function, which can be limited by the nature of the function itself.
Based on the usual characteristics of functions:
- A. Without further information, we can generally assume that f(x) has a domain of all real numbers unless specified otherwise.
- B. If g(x) is a function that only takes on negative values, then its range would indeed be y < 0.
- C. Similarly, if h(x) is defined such that it only takes positive values, then the statement about its range being y > 0 would be correct.
- D. If g(x) does not involve division by zero or other undefined operations, then its domain can be all real numbers.
- E. If h(x) includes a square root or any operation that requires positive numbers, then it would have a domain of x > 0.
To accurately determine the domain and range of these functions, a complete definition of each function is necessary. Nonetheless, the above statements are often true for typical types of functions.