The problem asks: Which graph represents a function?

To determine this, we use the vertical line test:

• If any vertical line intersects the graph at more than one point, it is not a function.
• If every vertical line intersects the graph at most one point, it is a function.

Analyzing each graph:

1. Graph (a):

   • This graph fails the vertical line test because a vertical line crosses the curve at more than one point in several locations.
     Conclusion: Not a function.

2. Graph (b):

   • This graph passes the vertical line test since no vertical line intersects the graph more than once.
     Conclusion: This is a function.

3. Graph (c):

   • This graph fails the vertical line test because a vertical line crosses the curve at multiple points.
     Conclusion: Not a function.

4. Graph (d):

   • This graph fails the vertical line test because the vertical line intersects the step at multiple points.
     Conclusion: Not a function.

Final Answer:

Graph (b) represents a function because it passes the vertical line test.

Would you like me to explain the vertical line test in more detail or clarify anything further?

Related Questions:

1. What is the definition of a function in mathematics?
2. Can a function have two inputs (x-values) mapping to the same output (y-value)?
3. Why does the vertical line test work to determine if a graph is a function?
4. What is the difference between a function and a relation?
5. How would the graph of a linear function look compared to these graphs?

Tip: A function maps each input (x-value) to exactly one output (y-value). If a vertical line crosses a graph in more than one place, it means an input has more than one output, violating the definition of a function.