Understanding the Relation: Graphing Points and Finding Domain and Range
To graph the relation defined by the points (1, 12), (12, 132), and (0, 32), you can follow these steps:
1. Plotting the Points
Begin by setting up your Cartesian coordinate system (x-y plane). Each point you have corresponds to an (x, y) coordinate:
- (1, 12) – This means for x = 1, y = 12
- (12, 132) – For x = 12, y = 132
- (0, 32) – For x = 0, y = 32
Mark these points on your graph:
- (1, 12) will be located one unit to the right of the origin and twelve units up.
- (12, 132) will be further to the right, twelve units along the x-axis and one hundred thirty-two units up.
- (0, 32) is straight upward on the y-axis at thirty-two.
2. Drawing the Relation
Once you have plotted the points, you can connect them if desired to illustrate a relation. Since this includes a few distinct points, you can simply represent the relation using dots on the graph.
3. Finding the Domain
The domain of a relation consists of all the x-values from the points you plotted. From your points:
- x-values: 1, 12, 0
To organize this, the domain is: {0, 1, 12}.
4. Finding the Range
The range includes all the y-values from your plotted points:
- y-values: 12, 132, 32
Thus, the range is: {12, 32, 132}.
Conclusion
In summary, the process of graphing the relation of these points and identifying the domain and range is straightforward:
- Domain: {0, 1, 12}
- Range: {12, 32, 132}
This foundational understanding will serve you well as you explore more complex relations and data visualizations in mathematics.