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.