Let f : ℝ → ℝ be given by f(x) = x⁵ + 5x⁴ + 10x³ + 10x² + 3x + 1 for x < 0; f(x) = x² − x + 1 for 0 ≤ x < 1; f(x) = (2/3)x³ − 4x² + 7x − 8/3 for 1 ≤ x < 3; and f(x) = (x − 2)logₑ(x − 2) − x + 10/3 for x ≥ 3. Then which of the following options is/are correct?