https://file.aiquickdraw.com/mathbot/file/17292730368582k8o0041.jpg

Which graph showing the relation between 
x
 and 
y
 represents 
y
 as a function of 
x
? Select all that apply.

In this image, the task is to identify which graphs represent \( y \) as a function of \( x \). For \( y \) to be a function of \( x \), each value of \( x \) must correspond to exactly one value of \( y \). This means the graph must pass the **vertical line test**, where no vertical line intersects the graph at more than one point.

Let's analyze each option based on this criterion:

1. **Graph A**: The curve does not pass the vertical line test. A vertical line would intersect the curve at more than one point. Hence, **A** is not a function.
   
2. **Graph B**: The rays in the graph spread outwards and pass the vertical line test, as each vertical line touches the graph at exactly one point. **B** is a function.

3. **Graph C**: The graph has a curve similar to a sine wave, and it does not pass the vertical line test, as some vertical lines would intersect the graph at more than one point. **C** is not a function.

4. **Graph F**: This is a parabola opening downward, and it passes the vertical line test, as each vertical line intersects the graph at only one point. **F** is a function.

Therefore, the graphs that represent \( y \) as a function of \( x \) are **B and F**.

Do you want more details or have any questions?

Here are 5 related questions:
1. What is the vertical line test, and how does it work?
2. Why does a parabola always represent a function?
3. What kind of graph represents a non-function, and why?
4. Can multiple types of curves be functions, or are there restrictions?
5. How do we distinguish between one-to-one functions and many-to-one functions?

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

Which graph showing the relation between x and y represents y as a function of x? Select all that apply.

Learn how to identify which graphs represent y as a function of x by applying the vertical line test. This guide covers graph analysis and functions, suitable for students in Grades 9-12. Understand the core concept of determining functions visually through detailed analysis.

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