Example 5 Check the points where the constant function f(x) = k is continuous Solution The function is defined at all real numbers and by definition, its value at any
real number equals k Let c be any real number Then
lim
( )
x
c f x
→
 = lim
x
c k
k
→
=
Since f(c) = k = lim
x
c
→  f(x) for any real number c, the function f is continuous at
every real number