To determine the domain and range of a parabola, we typically look at the vertex and the direction in which the parabola opens (upward or downward).
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Domain:
- For any parabola, the domain is usually all real numbers unless there are specific constraints on \( x \). If the problem states that there are no x-restrictions, the domain is \( x \) is all real numbers (this would correspond to the option that states "Domain: x is all real numbers.").
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Range:
- The range of a parabola depends on its vertex and whether it opens upward (which means the range is from the vertex value to \( +\infty \)) or downward (which means the range is from \( -\infty \) to the vertex value).
- If the vertex is the highest point of the parabola and the maximum value is \( 6 \), then the range would be \( -\infty < y \leq 6 \).
Considering these points:
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If the vertex of the parabola is at \( (x, 6) \) and the parabola opens downwards (which typically would match the range \( -\infty < y \leq 6 \)), then the first choice of "Domain: x is all real numbers. Range: −∞<y≤6" can be true.
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If we see a limited interval such as \( -8 \leq x \leq 8 \) as part of the domain, then that would need to be the scenario when the graph is restricted, which is less common for basic parabolas unless otherwise stated.
Taking into account these assumptions, the likely correct answer based on typical characteristics of parabolas would be:
Domain: x is all real numbers. Range: −∞ < y ≤ 6.
However, you would need to double-check based on specific details of the graph provided in your course material.
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