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The leftmost line segment has a domain of -4 ≤ x < -1, or [-4, 1).
The central line segment has a domain of -1 ≤ x ≤ 2, or [-1, 2].
The rightmost line segment has a domain of 2 < x ≤ 5, or (2, 5].
Overall, this function has a domain of
[-4, 1) U [-1, 2] U (2, 5]
(where U means "union" in the set-theoretic notion)
But this also simplifies to the interval [-4, 5].
These correspond to the <u>first</u> and <u>last</u> choices.
<span>Given that the directrix of the parabola is at y = -8 and the focus is at point (8, 16), this means that the parabola opens upwards and the x part of the equation of the parabola is squared. The x-value of the vertex of a parabola is the same as the x-value of the focus while the y-value of the vertex is half the sum of y-values of the focus and the directrix. Therefore, the vertex of the given parabola is (8, (16 - 8)/2) = (8, 8/2) = (8, 4).</span>
