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Select all of the following graphs which represent y as a function of x

To determine which of the graphs represent \( y \) as a function of \( x \), we can apply the **Vertical Line Test**. This test states that a graph represents a function if and only if no vertical line intersects the graph at more than one point.

Let me analyze the graphs in the image and identify which ones meet this criterion.

1. **Graph A**: This graph does not pass the vertical line test as a vertical line would intersect the graph at multiple points.
   
2. **Graph B**: This graph passes the vertical line test, meaning it represents \( y \) as a function of \( x \).

3. **Graph C**: This graph does not pass the vertical line test.

4. **Graph D**: This graph passes the vertical line test.

5. **Graph E**: This graph does not pass the vertical line test.

6. **Graph F**: This graph passes the vertical line test.

### Summary:
- **Graphs that represent \( y \) as a function of \( x \)**: **B, D, F**

Would you like more details on how the Vertical Line Test works or have any other questions? 

Here are some related questions you might find helpful:
1. What is the definition of a function in mathematics?
2. How can we determine if a set of points represents a function?
3. What are some examples of real-life functions?
4. Can a circle on a graph represent a function?
5. What is the difference between a function and a relation?

**Tip:** Always remember that for a graph to represent a function, each input \( x \) must correspond to exactly one output \( y \).

Discover how to identify functions using the Vertical Line Test with clear examples. This page explains the criteria for a graph to represent y as a function of x and analyzes specific graphs (A, B, C, D, E, F). Learn why graphs B, D, and F meet the Vertical Line Test and represent y as a function of x. Suitable for high school students and anyone interested in mathematical functions.

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