To determine the domain and range of a function, we would typically analyze its graph. However, since the graph is not provided, I can explain how to approach these questions.

1. Domain:

• The domain refers to all the possible values of $x$ (input values) for which the function is defined.
• If the graph is a continuous curve or line and does not have any breaks, jumps, or undefined points, the domain is typically all real numbers or can be represented as a specific interval.
• If the graph has a restricted range of $x$-values (e.g., it only exists between $x = -4$ and $x = 4$), the domain will be represented by a compound inequality like $-4 \leq x \leq 4$.

2. Range:

• The range refers to all the possible values of $y$ (output values) for which the function has corresponding $x$-values.
• If the graph covers all possible $y$-values, the range will be all real numbers.
• If the graph has a restricted vertical range (e.g., the function's $y$-values only lie between certain limits), the range would be a compound inequality.

Answer Choices Breakdown:

• Part 1: Domain

  • A: $-4 \leq x \leq 4$ (This is a specific interval domain, meaning the function is only defined between $x = -4$ and $x = 4$.)
  • B: All real numbers (This means the function is defined for any $x$-value.)
  • C: The graph does not represent a function (This suggests the graph fails the vertical line test, which would make it not a function.)

• Part 2: Range

  • A: A specific inequality (This would represent a restricted vertical range, where the function only takes certain $y$-values.)
  • B: All real numbers (This means the function has no restrictions on its $y$-values.)
  • C: The graph does not represent a function (If the graph does not represent a function, we wouldn't discuss the range.)

Next Steps:

If you can provide a graph, I can give you more precise answers. If you're referring to a graph from a textbook or assignment, identifying whether the graph is continuous or has any breaks, and what the limits of the $x$- and $y$-values are, will help you select the correct options.

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Do you have a graph you can share to clarify the domain and range? Or do you have any further questions on these topics?

Related questions:

1. How do you identify the domain and range from a graph?
2. What is the vertical line test, and how does it determine if a graph represents a function?
3. How can you tell if a function has a restricted domain or range just by looking at its graph?
4. What is the difference between domain and range in a mathematical function?
5. How do you represent a range of values in compound inequality form?

Tip:

Always start by identifying if the graph has breaks, jumps, or other discontinuities, as these will affect the domain and range.