Check the points where the constant function $f(x)=k$ is continuous.

(A) The function $f(x) = k$ is defined for all real numbers $x \in \mathbb{R}$.
By definition,for any real number $c$,the value of the function is $f(c) = k$.
To check for continuity at $x = c$,we evaluate the limit:
$\lim_{x \to c} f(x) = \lim_{x \to c} k = k$.
Since $\lim_{x \to c} f(x) = f(c) = k$ for any arbitrary real number $c$,the function $f(x) = k$ is continuous at every point in its domain,which is the set of all real numbers $\mathbb{R}$.