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 x < 0, the function equals 3, so 3 is in the range. For 0 ≤ x < 2, x² + 2 takes values from 2 up to, but not including, 6. For x ≥ 2, ½x + 5 starts at 6 and increases without bound. Together, these outputs cover every value from 2 upward, so the range is [2, ∞), choice A.

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