Understanding Functions and Graphs

Oct 13, 2025 by miodeya.com 40 views

Which Ordered Pair Can Be Removed So That The Resulting Graph Represents A Function?

Understanding Functions and Graphs

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In the context of graphs, a function is a relation between a set of x-coordinates and a set of y-coordinates. The graph of a function is a set of points in the Cartesian plane, where each point represents an ordered pair (x, y). For a graph to represent a function, each x-coordinate must correspond to exactly one y-coordinate.

Vertical Line Test

One way to determine if a graph represents a function is to use the vertical line test. This test involves drawing a vertical line through the graph and checking if it intersects the graph at more than one point. If the vertical line intersects the graph at more than one point, then the graph does not represent a function. On the other hand, if the vertical line intersects the graph at exactly one point, then the graph represents a function.

Analyzing the Given Options

We are given four ordered pairs: A. (-4, -4), B. (-2, 2), C. (1, 3), and D. (5, -4). We need to determine which of these ordered pairs can be removed so that the resulting graph represents a function.

Option A: (-4, -4)

If we remove the ordered pair (-4, -4), the graph will still have multiple points with the same x-coordinate. For example, the points (-4, -3) and (-4, -5) will still be present in the graph. Therefore, removing the ordered pair (-4, -4) will not result in a graph that represents a function.

Option B: (-2, 2)

If we remove the ordered pair (-2, 2), the graph will still have multiple points with the same x-coordinate. For example, the points (-2, 1) and (-2, 3) will still be present in the graph. Therefore, removing the ordered pair (-2, 2) will not result in a graph that represents a function.

Option C: (1, 3)

If we remove the ordered pair (1, 3), the graph will no longer have multiple points with the same x-coordinate. The points (1, 2) and (1, 4) will no longer be present in the graph. Therefore, removing the ordered pair (1, 3) will result in a graph that represents a function.

Option D: (5, -4)

If we remove the ordered pair (5, -4), the graph will still have multiple points with the same x-coordinate. For example, the points (5, -3) and (5, -5) will still be present in the graph. Therefore, removing the ordered pair (5, -4) will not result in a graph that represents a function.

Conclusion

Based on the analysis of the given options, we can conclude that the ordered pair (1, 3) can be removed so that the resulting graph represents a function.

Key Takeaways

A function is a relation between a set of inputs and a set of possible outputs.
The graph of a function is a set of points in the Cartesian plane, where each point represents an ordered pair (x, y).
The vertical line test can be used to determine if a graph represents a function.
If a graph represents a function, each x-coordinate must correspond to exactly one y-coordinate.
Removing an ordered pair from a graph that represents a function will result in a graph that still represents a function, unless the removed ordered pair is the only one that corresponds to a particular x-coordinate.

Final Answer

The final answer is C. (1, 3).
Which Ordered Pair Can Be Removed So That The Resulting Graph Represents A Function? - Q&A

Understanding Functions and Graphs

Q: What is the vertical line test?

A: The vertical line test is a method used to determine if a graph represents a function. It involves drawing a vertical line through the graph and checking if it intersects the graph at more than one point. If the vertical line intersects the graph at more than one point, then the graph does not represent a function.

Q: How can I determine if a graph represents a function?

A: You can use the vertical line test to determine if a graph represents a function. If the vertical line intersects the graph at exactly one point, then the graph represents a function.

Q: What happens if I remove an ordered pair from a graph that represents a function?

A: If you remove an ordered pair from a graph that represents a function, the graph will still represent a function, unless the removed ordered pair is the only one that corresponds to a particular x-coordinate.

Q: Can I remove any ordered pair from a graph that represents a function?

A: No, you cannot remove any ordered pair from a graph that represents a function. If you remove an ordered pair that corresponds to a particular x-coordinate, the graph will no longer represent a function.

Q: How can I determine which ordered pair to remove from a graph that represents a function?

A: You can use the vertical line test to determine which ordered pair to remove from a graph that represents a function. If the vertical line intersects the graph at more than one point, then the graph does not represent a function. You can then remove the ordered pair that corresponds to the x-coordinate that intersects the graph at more than one point.

Q: What is the final answer to the problem?

A: The final answer is C. (1, 3).

Key Takeaways

A function is a relation between a set of inputs and a set of possible outputs.
The graph of a function is a set of points in the Cartesian plane, where each point represents an ordered pair (x, y).
The vertical line test can be used to determine if a graph represents a function.
If a graph represents a function, each x-coordinate must correspond to exactly one y-coordinate.
Removing an ordered pair from a graph that represents a function will result in a graph that still represents a function, unless the removed ordered pair is the only one that corresponds to a particular x-coordinate.

Frequently Asked Questions

Q: What is the vertical line test? A: The vertical line test is a method used to determine if a graph represents a function.
Q: How can I determine if a graph represents a function? A: You can use the vertical line test to determine if a graph represents a function.
Q: What happens if I remove an ordered pair from a graph that represents a function? A: If you remove an ordered pair from a graph that represents a function, the graph will still represent a function, unless the removed ordered pair is the only one that corresponds to a particular x-coordinate.

Conclusion

In conclusion, the ordered pair (1, 3) can be removed so that the resulting graph represents a function. The vertical line test can be used to determine if a graph represents a function, and removing an ordered pair from a graph that represents a function will result in a graph that still represents a function, unless the removed ordered pair is the only one that corresponds to a particular x-coordinate.