Determine whether the following relation represents a function. If the relation is a function then state domain and range?
{(-1,-6),(2,-6),(3,-6),(4,-6)}
Does the given relation represents a function?
What is domain?
Yes
To determine if the given relation represents a function, we need to check if each x-value (on the left side) corresponds to a unique y-value (on the right side). In other words, if any two ordered pairs have the same x-value but different y-values, then the relation is not a function.
Looking at the given relation:
{(-1,-6),(2,-6),(3,-6),(4,-6)}
We can see that all the x-values (-1, 2, 3, 4) are unique, but the y-values (-6) are the same for all the ordered pairs. Since each x-value is associated with the same y-value, the relation is a function.
The domain of a function is the set of all possible input values (x-values) in the relation. In this case, since all the x-values are given in the relation, the domain is {-1, 2, 3, 4}.
For a function where each x-value is associated with a unique y-value, the range is the set of all possible output values (y-values). In this case, since all the y-values are the same (-6), the range is {-6}.
To determine whether the given relation represents a function, we need to check if each input (x-value) in the relation is paired with a single output (y-value) and not repeated.
In the given relation {(-1,-6),(2,-6),(3,-6),(4,-6)}, we can observe that each input (-1, 2, 3, 4) is paired with the output value -6. Hence, every x-value in the relation has a unique corresponding y-value.
Therefore, the given relation is indeed a function because each input has a unique output.
Next, let's find the domain of the function. The domain of a function refers to all the possible input values (x-values) in the relation.
From the given relation {(-1,-6),(2,-6),(3,-6),(4,-6)}, we can identify that the x-values in the relation are -1, 2, 3, and 4. Hence, the domain of the function is {-1, 2, 3, 4}.
Finally, let's determine the range of the function. The range of a function refers to all the possible output values (y-values) in the relation.
In this case, we can see that the y-value is always -6, regardless of the input. So, the range of the function is {-6}.
To summarize:
- The given relation represents a function because each input has a unique output.
- The domain of the function is {-1, 2, 3, 4}.
- The range of the function is {-6}.