. Determine whether each set of ordered pairs defines a function. Why or why not?  State the domain and range.
a) {(-2,0),(0,2),(1,7),(3,6),(1,5)}

To determine whether a set of ordered pairs defines a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). A function cannot have the same x-value paired with different y-values.

Given the set of ordered pairs: \(\{(-2,0),(0,2),(1,7),(3,6),(1,5)\}\):

1. Check for duplicate x-values with different y-values.
2. Identify the domain (the set of all x-values).
3. Identify the range (the set of all y-values).

### Checking if the set is a function:
- The pair \((1,7)\) has \(x = 1\).
- The pair \((1,5)\) also has \(x = 1\).

Since the x-value \(1\) corresponds to two different y-values (7 and 5), this set does not define a function.

### Domain:
The domain is the set of all x-values:
\[ \{-2, 0, 1, 3\} \]

### Range:
The range is the set of all y-values:
\[ \{0, 2, 7, 6, 5\} \]

### Summary:
- This set does **not** define a function because the x-value \(1\) is paired with two different y-values (7 and 5).
- Domain: \(\{-2, 0, 1, 3\}\)
- Range: \(\{0, 2, 7, 6, 5\}\)

Do you want details or have any questions? 

Here are 5 numbered questions for you to ask:
1. Can you explain more about functions and their properties?
2. How do you determine the domain and range of a function?
3. What are some examples of sets that do define functions?
4. How do you graph a set of ordered pairs to visualize a function?
5. Can you explain the vertical line test for functions?

Tip: When identifying whether a set of ordered pairs defines a function, always check for unique x-values first. If any x-value repeats with different y-values, it is not a function.

Learn how to determine if a set of ordered pairs defines a function, including identifying the domain and range. This problem explores the concept of functions in mathematics and provides step-by-step analysis. Suitable for Grades 9-12.

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