By inspection, it seems prudent
to partition the domain of definition of f into
three disjoint subsets of the real line Let
D1 = {x ∈ R : x < 0}, D2 = {0} and
D3 = {x ∈ R : x > 0}
Case 1 At any point in D1, we have f(x) = x2 and it is easy to see that it is continuous
there (see Example 2) Case 2 At any point in D3, we have f(x) = x and it is easy to see that it is continuous
there (see Example 6) Fig 5