is a function {(1, 2), (3, 6), (4, -7), (6, -10)}
The given set of ordered pairs {(1, 2), (3, 6), (4, -7), (6, -10)} can represent a function if each x-value (first element in each pair) is unique. To determine if the given set of ordered pairs represents a function, we can check if there are any repeating x-values.
In this case, there are no repeating x-values. Therefore, the given set {(1, 2), (3, 6), (4, -7), (6, -10)} does form a function.
To determine if a function exists based on the given set of ordered pairs, let's follow these steps:
Step 1: Check for uniqueness
Check if each first element in the ordered pairs is unique. In this case, the first elements are {1, 3, 4, 6}, and all of them are unique.
Step 2: Verify if each first element is associated with only one second element
Next, check whether each first element is associated with only one second element. In this case, the first element 1 is associated with 2, 3 is associated with 6, 4 is associated with -7, and 6 is associated with -10. Since there is only one second element for each first element, this condition is satisfied.
Step 3: Determine if the function is well-defined
Verify if the function is well-defined by checking that the second element is unique for each first element. In this case, there are no repeated second elements, so the function is well-defined.
Step 4: Conclusion
Based on the above analysis, the given set of ordered pairs {(1, 2), (3, 6), (4, -7), (6, -10)} represents a well-defined function.
The given set of points {(1, 2), (3, 6), (4, -7), (6, -10)} represents a collection of points in a coordinate system. Each point in this set consists of an x-coordinate (the first number) and a y-coordinate (the second number).
To determine if this set of points represents a function, we need to check if every input (x-coordinate) has a unique output (y-coordinate).
To confirm if this set of points represents a function, we can follow these steps:
1. Arrange the points in ascending order based on the x-coordinates: {(1, 2), (3, 6), (4, -7), (6, -10)}.
2. Check if any x-coordinate is repeated in the set. In this case, none of the x-coordinates are repeated, so there are no duplicates.
3. Since there are no repeated x-coordinates, we can conclude that each x-coordinate has a unique corresponding y-coordinate.
4. Therefore, the given set of points {(1, 2), (3, 6), (4, -7), (6, -10)} represents a function.
In terms of the function itself, we can express it as f(x) = y, where:
f(1) = 2
f(3) = 6
f(4) = -7
f(6) = -10
Please note that the given set of points only provides a limited number of values for the function. To define the function more precisely, you would need to know the pattern or equation that generates the y-coordinate for any given x-coordinate.