https://file.aiquickdraw.com/mathbot/file/1729472107287tcc3j3rz.jpg

The task in the image asks to determine whether each graph represents a function. To assess this, we can apply the **vertical line test**: a graph represents a function if and only if no vertical line can intersect the graph at more than one point at a time.

Let's analyze each graph:

1. **Gráfico 1**: The vertical line test shows multiple points on a single vertical line (for example, around \(x = 1\)). Therefore, **this is not a function**.
   
2. **Gráfico 2**: Any vertical line drawn will intersect the graph at only one point. Hence, **this is a function**.

3. **Gráfico 3**: A vertical line can intersect the graph in multiple places (for instance, near \(x = 0\)). **This is not a function**.

4. **Gráfico 4**: Several vertical lines intersect more than one point (for example, \(x = -1\)). **This is not a function**.

5. **Gráfico 5**: Every vertical line intersects the graph at most once. Hence, **this is a function**.

6. **Gráfico 6**: A vertical line intersects the graph at multiple points (such as near \(x = 1\)). Therefore, **this is not a function**.

If you would like more details or have further questions, let me know!

Here are 5 related questions to explore the topic further:
1. What are the key characteristics of a function in terms of domain and range?
2. How does the vertical line test relate to the definition of a function?
3. Can a horizontal line test be applied to check if a graph is a one-to-one function?
4. How do transformations (shifting, reflecting) affect whether a graph represents a function?
5. What are some real-world examples where we need to determine if a relation is a function?

**Tip**: Always apply the vertical line test to quickly verify if a graph represents a function!

Determine if each graph represents a function using the vertical line test.

In this problem, students are asked to determine whether each graph represents a function by applying the vertical line test. This task involves understanding functions and how graphs can be used to visually determine the nature of a mathematical relationship. Suitable for students in Grades 9-11.

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