To determine the domain and range of the function shown in the graph:

1. Domain (possible x-values):

   • The graph stretches indefinitely in both the positive and negative $x$-directions.
   • Therefore, the domain is:
     $(-\infty, \infty)$
     This means the graph includes all real numbers for $x$.

2. Range (possible y-values):

   • The graph is a downward-opening parabola. The maximum point (vertex) occurs at $y = 6$.
   • The parabola extends downward indefinitely, so the $y$-values are less than or equal to 6.
   • Therefore, the range is:
     $(-\infty, 6]$

Final Answer:

• Domain: $(-\infty, \infty)$
• Range: $(-\infty, 6]$

Do you want further explanations about parabolas or how to identify the vertex? Let me know!

Related Questions:

1. How do you determine the vertex of a parabola from its graph?
2. What is the standard form of a quadratic function?
3. How can you find the axis of symmetry from a parabola?
4. How do you identify whether a parabola opens upward or downward?
5. How do you calculate the domain and range algebraically for any quadratic equation?

Tip: The domain of any quadratic function is always all real numbers, but the range depends on the vertex and the parabola's direction.