If f(x)=6 for all x∈A, which statement about f is correct?

Correct answer: f is a constant function

The governing concept is the definition of a constant function. A function assigns exactly one output to each input in its domain, and it is called constant when that output is the same for every input. Since f(x) = 6 for every x in A, every element of the domain is mapped to the fixed value 6. Therefore f is a constant function, so option A is correct. It is not an identity function, because an identity function satisfies f(x) = x, not f(x) = 6 for all x. The rule clearly defines a function, so option C is false. Nothing states that A is empty, so option D is also unjustified; even if A had particular elements, they would all map to 6.