Question

Find the domain and range of the graphed function.

A graph of a parabola that opens up. The vertex of the parabola is 0, negative 3.

Responses

domain: all real numbers; range:
Pick the answer below.

domain: ; range: all real numbers
Pick the answer below.

domain: all real numbers; range: all real numbers
Pick the answer below.

domain: ; range:

Answer 1

Given that the graph is a parabola that opens upwards with its vertex at (0, -3), we can determine the domain and range:

1. **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

2. **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.