The image you uploaded displays two graphs and asks for the domain and range of the functions shown in the graphs. Let me help you analyze each graph to determine their domain and range.

Graph A:

• The graph is a parabola that opens downward.
• Domain: The domain of a quadratic function like this is all real numbers because the parabola continues indefinitely to the left and right.
  • Domain of Graph A: $(-\infty, \infty)$.
• Range: The range is the set of y-values the graph attains. Since the parabola opens downwards, the maximum y-value is the vertex's y-coordinate, and it decreases from there.
  • Based on the graph, the maximum y-value seems to be 4, and it extends downward to negative infinity.
  • Range of Graph A: $(-\infty, 4]$.

Graph B:

• The graph is also a parabola, but this one opens upwards.
• Domain: As with Graph A, the domain is all real numbers.
  • Domain of Graph B: $(-\infty, \infty)$.
• Range: The minimum y-value is at the vertex, and the graph increases from there. Based on the graph, the minimum y-value appears to be -2.
  • Range of Graph B: $[-2, \infty)$.

Let me know if you want further clarification or if you'd like to discuss these answers in more depth!

Here are 5 related questions:

1. What is the general form of a quadratic equation?
2. How do you find the vertex of a parabola algebraically?
3. Can the domain of any quadratic function ever be restricted?
4. How does the direction a parabola opens affect its range?
5. What methods can be used to find the range of more complex functions?

Tip: Always check the vertex of a parabola for determining the range, as it gives you the maximum or minimum value, depending on the direction it opens!