The graph you've provided appears to represent a parabola.

Domain

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For parabolas that extend infinitely to the left and right, the domain includes all real numbers.

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

Range

The range of a function is the set of all possible output values (y-values). For this parabola, the vertex is at the highest point on the graph, which looks to be around $y = 4$. The parabola opens downward, meaning the range includes all real numbers from $-\infty$ up to the vertex's y-coordinate.

Range: $(-\infty, 4]$

Would you like more details or have any questions? Here are some related questions that might interest you:

1. How do you determine the vertex of a parabola?
2. How can you identify whether a parabola opens upwards or downwards?
3. What is the standard form of a quadratic equation?
4. How do you find the axis of symmetry for a parabola?
5. What are the implications of the discriminant in a quadratic function?

Tip: When analyzing the range of a parabola, always consider whether the parabola opens upwards or downwards, as this determines whether the range starts from the vertex and goes upwards or downwards.