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The image shows a math problem asking you to graph two sets of relations and then use the vertical line test to determine if the relation is a function. The task also asks you to connect the pairs in the order given.

### The Relations Given:
- **a.** \[(1, 3), (2, 6), (3, 9), (2, 12), (3, 15)\]
- **b.** \[(0, 0), (1, 1), (2, 4), (3, 9)\]

### Steps to Solve:
1. **Graph each pair of coordinates** on a Cartesian plane.
2. **Draw the vertical lines** across the graph to perform the vertical line test.
   - A relation is a function if no vertical line intersects the graph at more than one point.
3. **Connect the points** in the order given to analyze the relations.

### Analysis:
- **Relation a:** If graphed, this relation may fail the vertical line test because it has repeated x-values (e.g., x = 2 for both (2, 6) and (2, 12)), meaning the vertical line test will show that the graph intersects the line in more than one place for these values.
- **Relation b:** This relation is expected to pass the vertical line test, as all x-values are unique, meaning each x-value corresponds to exactly one y-value.

Would you like the graphs to be plotted, or do you have any other questions? 

### Related Questions:
1. How does the vertical line test determine if a relation is a function?
2. What happens if two points have the same x-value in a graph?
3. Can a function have more than one y-value for the same x-value?
4. How do you interpret the results of the vertical line test?
5. Why is it important to connect the points in the order given?

### Tip:
When performing the vertical line test, always check for any repeated x-values first, as these are the primary indicators that a relation might not be a function.

Graph the following relations and use the vertical line test to see if the relation is a function. Connect the pairs in the order given: a. (1,3), (2,6), (3,9), (2,12), (3,15) b. (0,0), (1,1), (2,4), (3,9).

Learn how to graph relations and use the vertical line test to determine if a relation is a function. This problem involves graphing points and analyzing whether the relation is a function by checking if any vertical line intersects the graph more than once.

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