https://file.aiquickdraw.com/mathbot/file/1729054500837p8ds1m3a.jpg

Yes, the graph does show a function.

Explanation: A graph represents a function if, for every value of \(x\), there is only one corresponding value of \(y\). This can be tested using the **Vertical Line Test**: if a vertical line drawn at any point on the graph intersects the curve at most once, then the graph represents a function.

In this case, no vertical line would intersect the red curve more than once at any given \(x\)-coordinate, which means this graph passes the Vertical Line Test and is therefore a function.

Would you like more details on this concept or have any questions?

Here are 5 related questions you might explore:
1. What is the Vertical Line Test, and why is it important in determining functions?
2. Can a graph fail the Vertical Line Test and still represent a relation?
3. How do you identify if a function is one-to-one using a horizontal line test?
4. What are the different types of functions, and how are their graphs different?
5. How do piecewise functions appear on a graph, and how do we test them for being functions?

**Tip:** Remember, every function has a unique \(y\)-value for each \(x\)-value, but not every relation is a function. Use the Vertical Line Test to quickly determine if a relation is a function.

Does the graph to the right show a function?

Understand how to determine if a graph represents a function by applying the Vertical Line Test. In this example, the graph passes the test, confirming that it is a function. Learn the importance of the test in graph analysis, suitable for Grades 8-10.

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