Find the domain and range of the graphed function.

Question

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

Answer 1

To determine the domain and range of the given parabola, we can analyze the features of the graph described.

1. Domain: A parabola that opens upwards does not have any restrictions on the x-values. It extends infinitely to the left and right. Therefore, the domain of the function is all real numbers.

   Domain: \( (-\infty, \infty) \)

2. Range: The vertex of the parabola is given as (0, -3). Since the parabola opens upwards, the y-values will start at the y-coordinate of the vertex and extend infinitely upwards. Thus, the minimum value of the function occurs at the vertex, which is -3.

   Therefore, the range of the function is all y-values greater than or equal to -3.

   Range: \( [-3, \infty) \)

In summary:

• Domain: \( (-\infty, \infty) \)
• Range: \( [-3, \infty) \)