I see that you've uploaded a worksheet titled "Domain, Range, & Functions." The sheet includes several tasks, such as determining the domain and range of various relations.

Let's walk through some examples to confirm your work or help with questions:

For the first section:

• Problem 1: Relation: $(0,1), (2,4), (4,7), (9,1)$

  • Domain: {0, 2, 4, 9}
  • Range: {1, 4, 7}

  Your answers look good!

• Problem 2: Relation: $(1,2), (2,4), (3,1), (4,5), (7,9)$

  • Domain: {1, 2, 3, 4, 7}
  • Range: {1, 2, 4, 5, 9}

  Also correct!

The rest of the problems seem similarly completed. If you'd like, I can assist with the remaining problems or verify the other answers.

For the second section (relation tables and graphs):

Each table or graph represents pairs $(x, y)$. You will need to:

• Write the set of ordered pairs $(x, y)$,
• Identify the domain (the set of all x-values),
• Identify the range (the set of all y-values).

I can help walk through these as well, or if there is a specific question you need clarification on, feel free to point it out.

Would you like me to go over any specific question or provide further details?

5 Follow-up Questions:

1. Can you explain how the domain and range differ when the relation is shown on a graph versus a table?
2. What are the key characteristics of a function, and how do they relate to the domain and range?
3. How would you identify whether a relation is a function based on its ordered pairs?
4. Could a range ever contain the same value more than once? If so, in what case?
5. How does the vertical line test help in determining if a relation is a function?

Tip:

To find the domain, remember that it's always the set of all possible x-values, and the range is the set of all possible y-values. Always list the values without repeating them!