Question

Determine the domain & range for the graph: (1 point) Responses Domain: −8≤x≤8 . Range: −∞<y≤6 Domain: −8≤x≤8 . Range: −∞<y≤6 Domain: x is all real numbers. Range: −∞<y≤6 Domain: x is all real numbers. Range: −∞<y≤6 Domain: x is all real numbers. Range: −10≤y≤6

The vertex curves at 6 on the y axis

Answer 1

To determine the domain and range of the graph based on the information you've provided, let's analyze it.

1. **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.

2. **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**.

3. **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:
- If the graph is restricted in the x-direction to between -8 and 8:
- Domain: −8≤x≤8
- Range: −∞<y≤6

- 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.