To graph a relation and its inverse, you first need to understand what the relation and its inverse represent. A relation typically consists of pairs of input values (x) and output values (y). The inverse of this relation swaps these x and y values.
Here’s a step-by-step guide:
- Plot the original relation: Start by plotting the points of the original relation on a coordinate plane. For instance, if you have points like (1, 2), (2, 3), and (3, 4), plot these accurately on your graph.
- Identify the inverse points: To find the inverse points, simply swap the x and y values of each point from the relation. For the examples given, the inverse points would be (2, 1), (3, 2), and (4, 3).
- Graph the inverse using open circles: For the inverse points, plot them on the same graph but use open circles to differentiate them from the original relation. This way, it’s clear which points belong to the inverse.
- Connect the points: If needed, you can connect the original relation points with a solid line, while the inverse points can either remain as open circles or be connected with a dashed line, depending on whether you’re showing a continuous function or just discrete points.
By following these steps, you’ll create a clear visual representation of both the relation and its inverse, showcasing how they are related to each other. Remember, the main concept is that the inverse flips the roles of the x and y coordinates, and using open circles helps to indicate that these points are from the inverse.