Which of the following accurately shows the range of the given function? f of x equals enlarged left-brace first row 3 comma x less than 0. Second row x squared plus 2 comma 0 less than or equal to x less than 2. Third row one half x plus 5 comma x greater than or equal to 2.

For 0 ≤ x < 2, x² + 2 ranges from 2 up to, but not including, 6. For x ≥ 2, ½x + 5 starts at 6 and increases without bound, giving [6, ∞). The constant piece contributes only 3, which is already in that combined range, so the full range is [2, ∞), choice D.

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