From the graph you provided, it appears to be a parabola that opens upwards. Let's identify the domain and range based on the features of the parabola.

Domain:

The domain of a parabola like this is the set of all possible $x$-values for which the function is defined. Since the parabola extends infinitely in both directions along the $x$-axis, the domain is all real numbers.

Domain: $(-\infty, \infty)$ or in interval notation, $x \in \mathbb{R}$.

Range:

The range of a function is the set of all possible $y$-values. In this graph, the parabola has its lowest point at $y = 0$ and opens upwards. Thus, the $y$-values start from 0 and increase without bound.

Range: $[0, \infty)$ or $y \geq 0$.

Would you like more details on how to interpret this graph?

Here are 5 related questions to deepen your understanding:

1. How do we determine the vertex of a parabola from its equation or graph?
2. What is the equation of this parabola based on the graph?
3. How do you find the axis of symmetry of a parabola?
4. How does the direction (upward or downward) of the parabola affect its range?
5. What are the properties of a quadratic function that describe its behavior?

Tip:

When identifying the domain and range of a parabola, always consider whether it opens upwards or downwards, as this influences whether the range is limited from below or from above.