The image shows a graph of a quadratic function with a downward-facing parabola and corresponding questions related to its domain, range, and other characteristics.

Here's a breakdown of the key points:

1. Domain: The domain of the function is "all real numbers." Since the graph of the parabola extends indefinitely left and right, the function is defined for every value of $x$.
2. Minimum $y$-value: Based on the parabola, it appears that the minimum $y$-value is at $y = 3$, as highlighted on the graph where $(1, 3)$ is shown as a point.
3. Range: The range of the function is "a subset of all real numbers." The lowest point is $y = 3$ and it opens downwards, so the function's values are all less than or equal to 3. Therefore, the correct range is $y \leq 3$.

The inequality provided for the range $y \leq 3$ should replace the incorrect $y = 0$.

Do you have any other questions about this? I can also provide more details on:

1. How to calculate the domain and range for other types of functions.
2. How to find the vertex of a quadratic function from its equation.
3. Understanding how a parabola's direction (up or down) affects its minimum and maximum values.
4. Writing the equation of a parabola given its graph.
5. Determining intercepts (both x- and y-intercepts) from the graph of a function.

Tip: When dealing with quadratic functions, remember that if the parabola opens upwards, the vertex is the minimum point, and if it opens downwards, the vertex is the maximum point!