The domain of the graphed function A. x is all real numbers. Therefore, A. x is all real numbers is correct .
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined and yields valid output values (y-values).
When the domain is stated as "all real numbers," it signifies that the function is defined and meaningful for any real value of x.
This implies a continuous and unbroken graph, covering the entire real number line without any gaps, holes, or points of undefined behavior.
In a graphical context, an illustration of a function with a domain encompassing all real numbers suggests that, as you traverse the x-axis, there are no excluded values or regions where the function becomes undefined.
Each x-value corresponds to a valid y-value, creating a smooth and uninterrupted curve.
The absence of restrictions in the domain implies that the function's behavior is well-behaved across its entire range.
This characteristic is particularly common in polynomial functions, exponential functions, and many elementary mathematical expressions.
The clarity and comprehensiveness of a domain spanning all real numbers contribute to the versatility and applicability of the function in various mathematical and real-world contexts.