Domain and Range of the Set of Points

Oct 13, 2025 by windailys.com 137 views

Domain and Range of the Set of Points

To determine the domain and range of the set of points, we need to identify the x-coordinates and y-coordinates of the points, respectively.

Domain: The domain of a set of points is the set of all x-coordinates. In this case, the x-coordinates are -1, 0, 0, 6, and 7. Therefore, the domain of the set of points is $${-1,0,6,7}$$.
Range: The range of a set of points is the set of all y-coordinates. In this case, the y-coordinates are -2, -3, 2, -2, and -7. Therefore, the range of the set of points is $${-7,-3,-2,2}$$.

Is it a Function or Relation?

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. In other words, a function is a relation where every element of the domain maps to exactly one element of the range.

To determine if the set of points is a function, we need to check if each x-coordinate maps to exactly one y-coordinate.

Checking for uniqueness: We can see that the x-coordinate -1 maps to the y-coordinate -2, the x-coordinate 0 maps to both y-coordinates -3 and 2, the x-coordinate 6 maps to the y-coordinate -2, and the x-coordinate 7 maps to the y-coordinate -7. Since the x-coordinate 0 maps to two different y-coordinates, the set of points is not a function.

Finding $$f(-1)$$

Since the set of points is not a function, we cannot find $$f(-1)$$ in the classical sense. However, we can still find the value of the function at x = -1 by looking at the point (-1, -2) in the set of points.

Finding $$f(-1)$$: Since the point (-1, -2) is in the set of points, we can conclude that $$f(-1) = -2$$.

In conclusion, the domain of the set of points is $${-1,0,6,7}$$, the range is $${-7,-3,-2,2}$$, it is not a function, and $$f(-1) = -2$$.

Example Use Case

Suppose we have a set of points representing the temperature readings at different locations. The x-coordinate represents the location, and the y-coordinate represents the temperature. In this case, the domain would represent the set of locations, and the range would represent the set of possible temperatures.

Domain: The domain would be the set of locations, which could be a list of city names or coordinates.
Range: The range would be the set of possible temperatures, which could be a list of temperature values.
Function or Relation: If each location has a unique temperature reading, then the set of points would be a function. However, if some locations have multiple temperature readings, then the set of points would be a relation.
Finding $$f(-1)$$: If we want to find the temperature at a specific location, we can look up the point corresponding to that location in the set of points. For example, if we want to find the temperature at location -1, we can look up the point (-1, -2) in the set of points and conclude that the temperature at location -1 is -2.

Conclusion

In this article, we considered a set of points and determined its domain and range. We also checked if the set of points is a function or relation and found $$f(-1)$$. The domain of the set of points is $${-1,0,6,7}$$, the range is $${-7,-3,-2,2}$$, it is not a function, and $$f(-1) = -2$$. We also provided an example use case to illustrate the concept of domain, range, and function in a real-world scenario.

References

[1] "Functions and Relations." Khan Academy, Khan Academy, www.khanacademy.org/math/algebra-functions-and-graphs/functions-and-relations.

Keywords

Domain
Range
Function
Relation
Set of points
X-coordinate
Y-coordinate
Uniqueness
Temperature readings
Location
Temperature
Function or relation
Finding $$f(-1)$$