The question in the image is asking about whether a given graph represents a function, and then about the domain of that function.

• Is this the graph of a function? You selected "Yes." This suggests that the graph passed the vertical line test, meaning it represents a function (each x-value corresponds to exactly one y-value).

• What is the domain?

  • Option A asks for the domain in the form of an inequality or a compound inequality.
  • Option B states "The domain is all real numbers," meaning there are no restrictions on the x-values.
  • Option C claims "The graph does not represent a function," which does not apply since you selected "Yes" earlier.

To select the correct domain, you would need to examine the range of x-values the graph covers. If the graph stretches across the entire x-axis with no breaks or restrictions, the domain would likely be all real numbers (Option B). If the x-values are restricted (e.g., the graph only exists between two specific x-values), you'd need to input those values as an inequality (Option A).

Would you like further assistance with analyzing the specific graph?

Here are five questions to expand your understanding:

1. How can you use the vertical line test to determine if a graph represents a function?
2. What are some common domain restrictions for functions (e.g., square roots, rational functions)?
3. How do you represent domain restrictions using inequalities?
4. If a graph has endpoints or breaks, how does that affect the domain?
5. Can a function have a domain that is not all real numbers, but still be continuous?

Tip: Always check for any breaks or holes in a graph to ensure there are no restrictions on the domain.