Final answer:
The domain of the function is all real numbers except x = 3, and the range is all real numbers greater than or equal to zero.
Step-by-step explanation:
The domain of a function represents the set of all possible values for the independent variable (x), while the range represents the set of all possible values for the dependent variable (y). To find the domain and range of the function f(x) = x² - 9/(x-3), we need to consider any restrictions on the input values (x) and analyze the behavior of the function.
The function f(x) is defined for all real numbers except x = 3, where the denominator would become zero. Therefore, the domain of f(x) is the set of all real numbers excluding x = 3.
To determine the range, we can analyze the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity, the function approaches positive infinity. As x approaches negative infinity, the function also approaches positive infinity. Therefore, the range of f(x) is all real numbers greater than or equal to zero.