Given that the graph is a parabola that opens upwards with its vertex at (0, -3), we can determine the domain and range:
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Domain: The domain of a parabola is always all real numbers, regardless of its vertex or direction. This is because for any real number input (x-value), there is a corresponding output (y-value).
- Domain: all real numbers
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Range: Since the parabola opens upwards and has its vertex at (0, -3), the lowest point on the graph is at y = -3. This means the range includes all y-values starting from -3 and going up to positive infinity.
- Range: \( y \geq -3 \) (in interval notation, this is \([-3, \infty)\))
Thus, the domain and range of the function are:
- Domain: all real numbers
- Range: \( y \geq -3 \) or \([-3, \infty)\)
Select the response that states:
- Domain: all real numbers; range: \( y \geq -3 \) (if available) or simply indicate that the range starts from -3 and goes to infinity.