Which graph represents the same relation as the set \{\((-3,2),(5,5),(3,3),(3,-2)\)\}?
Answer (1)
The problem requires identifying a graph that represents the set of points {( − 3 , 2 ) , ( 5 , 5 ) , ( 3 , 3 ) , ( 3 , − 2 )} .
Each point is plotted on the coordinate plane.
The correct graph contains only these four points.
The graph representing the relation consists of the discrete points: {( − 3 , 2 ) , ( 5 , 5 ) , ( 3 , 3 ) , ( 3 , − 2 )} .
Explanation
Understanding the Problem The problem asks us to identify the graph that corresponds to the given set of ordered pairs: { ( − 3 , 2 ) , ( 5 , 5 ) , ( 3 , 3 ) , ( 3 , − 2 ) } . This means we need to find a graph that includes exactly these four points and no others.
Plotting the Points To solve this, we would typically plot each of these points on a coordinate plane and then visually compare this plot to the provided graphs. The correct graph will have all four points plotted correctly and no additional points.
Identifying the Quadrants The points are:
(-3, 2): This point is in the second quadrant.
(5, 5): This point is in the first quadrant.
(3, 3): This point is in the first quadrant.
(3, -2): This point is in the fourth quadrant.
Recognizing the Relation By plotting these points, we can see the relation they form. The key is to recognize that the relation is simply a set of discrete points.
Conclusion Therefore, the graph that represents the relation will consist of only these four points.
Examples
Understanding relations and their graphical representations is fundamental in many areas. For instance, in data analysis, each point in a scatter plot represents a data point, and understanding the relation between these points helps in drawing conclusions about the data. Similarly, in physics, plotting experimental data helps visualize relationships between variables, such as the relationship between the force applied to a spring and its extension. This exercise reinforces the ability to accurately represent discrete data graphically, which is a crucial skill in various scientific and analytical fields.
