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Write F if function and NF if not function in a given problem.

To determine if the given set of points represents a function, we can apply the vertical line test. A relation is a function if for each input (x-coordinate), there is exactly one output (y-coordinate). In other words, no two points should have the same x-coordinate with different y-coordinates.

Let's analyze the points:

\[
\{(6, 0), (-12, -16), (-6, 10), (20, -7)\}
\]

- For \(x = 6\), \(y = 0\).
- For \(x = -12\), \(y = -16\).
- For \(x = -6\), \(y = 10\).
- For \(x = 20\), \(y = -7\).

Each x-coordinate is unique, meaning no x-value has more than one corresponding y-value. Therefore, **this is a function**.

Answer: **F (Function)**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the vertical line test and how is it used to identify functions?
2. How would the result change if two points shared the same x-coordinate but had different y-values?
3. What are the characteristics of a one-to-one function?
4. Can you define a function in terms of its domain and range?
5. How would you graphically represent the given set of points?

**Tip:** When determining if a relation is a function, always check that no two points share the same x-value with different y-values!

Learn how to determine if a set of points {(6, 0), (-12, -16), (-6, 10), (20, -7)} represents a function using the vertical line test. This step-by-step solution explains how to identify functions by ensuring each input (x-coordinate) has a unique output (y-coordinate). Suitable for Grades 7-10.

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