Final answer:
The domain of the quadratic function f(x) = 3x² + 6x + 9 is all real numbers, expressed as (-∞, ∞) in interval notation.
Step-by-step explanation:
To state the domain of the function f(x) = 3x² + 6x + 9, we need to consider the type of function it is. Since this function is a quadratic function, its graph is a parabola. The domain of a quadratic function is all real numbers because there are no restrictions on the values that x can take to produce a real number output. Therefore, the domain of f(x) = 3x² + 6x + 9 is all real numbers, which can be written in interval notation as (-∞, ∞).