Final answer:
The domain of the function f(x) = x³ + 6x² − 19 is all real numbers, represented in interval notation as (-∞, +∞).
Step-by-step explanation:
The domain of a function indicates all the possible input values (x-values) for which the function is defined. In the case of the polynomial function f(x) = x³ + 6x² − 19, it is defined for all real numbers because there are no restrictions such as square roots of negative numbers or division by zero that would limit the values of x.
Thus, in interval notation, the domain of the function f(x) is (-∞, +∞), which represents all real numbers.