To determine the domain and range of a parabola, we generally consider its orientation (upward or downward) and vertex position.
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Domain:
- For parabolas, the domain is typically all real numbers unless there is a restriction on the x-values (like in a specific interval). However, since a standard parabola opens infinitely to the sides, the domain is often given as \( x \text{ is all real numbers} \).
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Range:
- If the parabola opens upwards, the range will be from the y-coordinate of the vertex to infinity.
- If it opens downwards, the range will be from negative infinity to the y-coordinate of the vertex.
From the provided options:
- Domain: x is all real numbers. Range: −∞<y≤6
- Domain: −8≤x≤8. Range: −∞<y≤6
- Domain: x is all real numbers. Range: −10≤y≤6
Assuming that the vertex of the parabola is at the top (since the maximum y-value is 6), then the range should correctly be from negative infinity up to and including 6.
Thus, the correct choice would be:
Domain: x is all real numbers. Range: −∞<y≤6
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