https://file.aiquickdraw.com/mathbot/file/1722433860124z3kv8h8w.png

To determine whether each set of ordered pairs on the graph represents a function, we need to check if each \( x \)-value is paired with exactly one \( y \)-value. This is often referred to as the "vertical line test" — if any vertical line crosses the graph more than once, the set of points does not represent a function.

### Graph 1
In the first graph, let's check the \( x \)-values:
- \( x = -16 \) is paired with \( y = 16 \).
- \( x = -8 \) is paired with \( y = -12 \).
- \( x = 0 \) is paired with \( y = -4 \).
- \( x = 8 \) is paired with \( y = 4 \).
- \( x = 16 \) is paired with \( y = 12 \).

Each \( x \)-value is associated with exactly one \( y \)-value, so the first graph **does** represent a function.

### Graph 2
In the second graph, let's check the \( x \)-values:
- \( x = 2 \) is paired with \( y = 3 \) and \( y = 12 \).
- \( x = 10 \) is paired with \( y = 6 \).
- \( x = 14 \) is paired with \( y = 9 \).
- \( x = 18 \) is paired with \( y = 5 \).

The \( x \)-value of 2 is paired with two different \( y \)-values (3 and 12). Therefore, the second graph **does not** represent a function.

### Graph 3
In the third graph, let's check the \( x \)-values:
- \( x = 1 \) is paired with \( y = -3 \).
- \( x = 3 \) is paired with \( y = 1 \).
- \( x = 5 \) is paired with \( y = -3 \).
- \( x = 7 \) is paired with \( y = 2 \).

Each \( x \)-value is associated with exactly one \( y \)-value, so the third graph **does** represent a function.

To summarize:
1. Graph 1: Represents a function.
2. Graph 2: Does not represent a function.
3. Graph 3: Represents a function.

Would you like more details on any of these graphs, or do you have any questions?

### Related Questions
1. What is the vertical line test and how is it used to determine if a graph represents a function?
2. Can a function have the same \( y \)-value for different \( x \)-values?
3. How would you determine if a graph represents a function if the points are not clearly labeled?
4. What is the definition of a function in terms of sets and ordered pairs?
5. How can you visually identify if a set of points on a graph does not represent a function?
6. What are some examples of graphs that do not represent functions?
7. How can you modify a set of points to make sure it represents a function?
8. What are some real-world applications of functions and why are they important?

### Tip
When analyzing graphs to determine if they represent a function, always remember the vertical line test: If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Explore how to determine if graphs represent functions using the vertical line test. Includes detailed examples and explanations for each graph's analysis. Suitable for high school students and beyond.

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