At how many points is $f(x) = \begin{cases} x + 1, & x < 0 \\ x^{2}, & 0 \le x < 2 \\ 2x, & x \ge 2 \end{cases}$ not continuous?

Explanation

1. 01

   Each piece is a polynomial, so only the joins at 0 and 2 can break.

2. 02

   At 0: $0 + 1 = 1$ on the left, $0^{2} = 0$ on the right, a break. At 2: $2^{2} = 4 = 2 \times 2$, no break. So 1 point.