Final answer:
The domain of the function a(x)=3x−1 is all real numbers, as there are no mathematical constraints limiting the value of x.
Step-by-step explanation:
The domain of a function represents all the possible values of x that the function can accept. In the case of a(x)=3x−1, this is a linear function, which means that it can accept any real number value for x. There are no restrictions like denominators that could be zero or square roots of negative numbers that can limit the domain in this context. Therefore, the domain of a(x) is all real numbers, which can be expressed using interval notation as (-∞, +∞).
The domain of a function signifies the set of allowable input values. For the linear function a(x) = 3x - 1, it lacks constraints such as denominators or square roots that impose limitations. Consequently, the domain encompasses all real numbers. The absence of restrictions implies that any real number can be assigned to x. In interval notation, this expansive domain is succinctly expressed as (-∞, +∞). This denotes an unbounded continuum, emphasizing the function's unrestricted applicability across the entire real number line, characteristic of linear functions without inherent constraints on the variable x.