To determine the domain and range of the graph based on the information you've provided, let's analyze it.
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Vertex at (h, k): You've mentioned that the vertex curves at 6 on the y-axis. Assuming the vertex is at the point (h, 6), this indicates the highest point of a downward-opening parabola.
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Domain: The domain is the set of all possible x-values that the function can take. You've given two domain options:
- Domain: −8≤x≤8
- Domain: x is all real numbers.
If the graph is indeed limited to the x-values between -8 and 8, then the domain would be −8≤x≤8. However, if the graph extends indefinitely on the x-axis, then the domain would be all real numbers.
- Range: The range is the set of all possible y-values that the function can take:
- Range: −∞<y≤6
- Range: −10≤y≤6
Since the vertex is at the highest point (6), and the graph opens downwards, the y-values would begin from negative infinity up to and including 6. Therefore, the range will be −∞<y≤6.
Conclusion:
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If the graph is restricted in the x-direction to between -8 and 8:
- Domain: −8≤x≤8
- Range: −∞<y≤6
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If the graph extends indefinitely in the x-direction:
- Domain: all real numbers
- Range: −∞<y≤6
Please choose the domain that corresponds to your specific graph. From your options, the range seems to be correctly identified as -∞ < y ≤ 6 based on the vertex at y = 6.