For the following relation, give the domain and range, and indicate whether it is a function.
{(1,2),(6,3),(3,1),(8,7)}
the domain is the set of 1st elements (x) of each pair.
the range is the set of 2nd elements (y).
It is a function if no x is paired with more than one y. That is, if each pair has a unique x.
Well, well, well! Let's dive into this relation, shall we?
The domain, my dear friend, is the set of all x-values. In this case, the x-values are 1, 6, 3, and 8. So, the domain is {1, 6, 3, 8}.
Now, let's move on to the range. The range, my friend, is the set of all y-values. In this case, the y-values are 2, 3, 1, and 7. So, the range is {2, 3, 1, 7}.
Now, the big question. Is this relation a function? Well, in a function, each x-value can only have one y-value assigned to it. And guess what? That's exactly the case with this relation! Each x-value in the set has a unique y-value associated with it. So, yes, this relation is indeed a function!
I hope my jolly explanation brought a smile to your face!
To determine the domain and range of a relation, we look at the x and y values respectively.
In this case, the x values are 1, 6, 3, and 8. Therefore, the domain of the relation is {1, 6, 3, 8}.
The y values are 2, 3, 1, and 7. So, the range of the relation is {2, 3, 1, 7}.
Now, let's determine if this relation is a function. A relation is considered a function if each input (x-value) has only one output (y-value).
Looking at the relation, each x-value has only one y-value associated with it. Therefore, this relation is indeed a function.
To determine the domain and range of the given relation, we need to look at the set of all x-coordinates (inputs) and y-coordinates (outputs) in the relation.
Domain:
Start by listing all the x-coordinates from the given relation: 1, 6, 3, and 8. The domain of the relation is the set of all these x-coordinates. Therefore, the domain for this relation is {1, 6, 3, 8}.
Range:
Next, list all the y-coordinates (outputs) from the given relation: 2, 3, 1, and 7. The range of the relation is the set of all these y-coordinates. Therefore, the range for this relation is {2, 3, 1, 7}.
Function:
To determine whether the relation is a function, we need to check if there is exactly one y-coordinate for each x-coordinate. In other words, no x-coordinate should be repeated in the relation.
Looking at the given relation: {(1,2), (6,3), (3,1), (8,7)}, we can see that there are no repeated x-coordinates. Each x-coordinate has a unique y-coordinate associated with it. Therefore, this relation is a function.
In summary, for the given relation:
Domain: {1, 6, 3, 8}
Range: {2, 3, 1, 7}
Function: Yes, it is a function.