The graph you've provided appears to represent a parabola, which is typically the graph of a quadratic function. In this case, the function seems to open downward with its vertex at the point (0, 5).

Domain:

The domain of a quadratic function is all real numbers since the function is defined for any input value of $x$.

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

Range:

The range refers to the set of possible values for $y$. Since the parabola opens downward and its vertex is at $y = 5$, the values of $y$ are less than or equal to 5.

Range: $(-\infty, 5]$

Would you like further details on how to find the domain and range for similar functions, or do you have additional questions related to this graph? Here are some questions to help expand your understanding:

1. How can we identify the domain and range of other types of functions, such as absolute value or rational functions?
2. What is the vertex form of a quadratic equation, and how does it relate to the graph?
3. How does the coefficient of a quadratic function affect the direction of the parabola?
4. How can you use the discriminant to determine the number of real roots of a quadratic equation?
5. What happens to the domain and range if the graph of the quadratic function is shifted horizontally or vertically?

Tip: For quadratic functions, the vertex provides key information about the range, and whether the parabola opens upward or downward affects the maximum or minimum value of the range.