12. What Is The Domain And Range Of The Following Set Of Points?$\{(-2,2),(-1,1),(0,0),(1,1),(2,2)\}$A. Domain: $x = \{-2,-1,0,1,2\}$ Range: $y = \{2,1,0,1,2\}$B. Domain: $x = \{2,1,0,1,2\}$ Range: $y =

Introduction

In mathematics, the domain and range of a set of points are crucial concepts that help us understand the behavior and characteristics of the points. The domain refers to the set of all possible input values (x-coordinates) of the points, while the range refers to the set of all possible output values (y-coordinates) of the points. In this article, we will explore the domain and range of a given set of points and discuss the correct answers to the provided options.

What is the Domain and Range of a Set of Points?

To determine the domain and range of a set of points, we need to examine the x-coordinates and y-coordinates of each point. The domain is the set of all unique x-coordinates, while the range is the set of all unique y-coordinates.

Analyzing the Given Set of Points

Let's analyze the given set of points: $\{(-2,2),(-1,1),(0,0),(1,1),(2,2)\}$. To determine the domain and range, we need to identify the unique x-coordinates and y-coordinates.

Domain

The domain is the set of all unique x-coordinates. Looking at the given set of points, we can see that the x-coordinates are: -2, -1, 0, 1, and 2. However, we notice that the x-coordinate 1 appears twice, but this does not affect the domain. The domain is simply the set of all unique x-coordinates.

Range

The range is the set of all unique y-coordinates. Looking at the given set of points, we can see that the y-coordinates are: 2, 1, 0, and 2. Again, we notice that the y-coordinate 2 appears twice, but this does not affect the range. The range is simply the set of all unique y-coordinates.

Conclusion

Based on our analysis, we can conclude that the domain of the given set of points is $x = \{-2,-1,0,1,2\}$, and the range is $y = \{2,1,0\}$. However, we notice that option A has a range of $y = \{2,1,0,1,2\}$, which is incorrect. The correct range should be $y = \{2,1,0\}$.

Discussion

Let's discuss the correct answers to the provided options.

Option A

Option A states that the domain is $x = \{-2,-1,0,1,2\}$ and the range is $y = \{2,1,0,1,2\}$. However, as we discussed earlier, the correct range should be $y = \{2,1,0\}$.

Option B

Option B states that the domain is $x = \{2,1,0,1,2\}$ and the range is $y = \{2,1,0\}$. However, the domain should be $x = \{-2,-1,0,1,2\}$, not $x = \{2,1,0,1,2\}$.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions about the domain and range of a set of points.

Q: What is the domain of a set of points?

A: The domain of a set of points is the set of all unique x-coordinates. It represents the possible input values of the points.

Q: What is the range of a set of points?

A: The range of a set of points is the set of all unique y-coordinates. It represents the possible output values of the points.

Q: How do I determine the domain and range of a set of points?

A: To determine the domain and range of a set of points, you need to examine the x-coordinates and y-coordinates of each point. The domain is the set of all unique x-coordinates, while the range is the set of all unique y-coordinates.

Q: What if a point has a repeated x-coordinate or y-coordinate?

A: If a point has a repeated x-coordinate or y-coordinate, it does not affect the domain or range. The domain and range are determined by the unique x-coordinates and y-coordinates, respectively.

Q: Can the domain and range be the same?

A: Yes, the domain and range can be the same. This occurs when all the x-coordinates and y-coordinates are unique and the same.

Q: How do I represent the domain and range mathematically?

A: The domain and range can be represented mathematically using set notation. For example, if the domain is $x = \{-2,-1,0,1,2\}$, it can be represented as $\{-2,-1,0,1,2\}$. Similarly, if the range is $y = \{2,1,0\}$, it can be represented as $\{2,1,0\}$.

Q: What is the importance of understanding the domain and range?

A: Understanding the domain and range is crucial in mathematics, as it helps us analyze and interpret the behavior of functions and relationships between variables. It also helps us identify the possible input and output values of a function.

Q: Can you provide an example of a set of points with a domain and range?

A: Let's consider the set of points $\{(1,2),(2,3),(3,4),(4,5)\}$. The domain of this set of points is $x = \{1,2,3,4\}$, and the range is $y = \{2,3,4,5\}$.

Conclusion

In conclusion, understanding the domain and range of a set of points is essential in mathematics. By following the steps outlined in this article, you can determine the domain and range of a set of points and represent them mathematically using set notation.