State the domain and range for the following relation. Then determine whether the relation represents a function. {(6,2), (-5,2) (9,7), (6,12)}
Express the relation {(-2, 1), (-1,0), (1,2), (2, 3), (3, 4)} as a table and as a mapping. Then, state the domain and range of the relation.
To determine the domain and range of the given relation {(6,2), (-5,2), (9,7), (6,12)}, we need to identify all the unique x-coordinates (domain) and y-coordinates (range) in the relation.
Domain: The unique x-coordinates in the relation are 6, -5, and 9. Therefore, the domain is {6, -5, 9}.
Range: The unique y-coordinates in the relation are 2, 7, and 12. Therefore, the range is {2, 7, 12}.
Now, to determine whether the relation represents a function, we need to check if each input x-value corresponds to only one output y-value.
In the given relation, we observe that the x-coordinate 6 appears twice, with corresponding y-coordinates of 2 and 12. This violates the definition of a function, as one x-value should correspond to only one y-value.
Hence, the relation {(6,2), (-5,2), (9,7), (6,12)} does not represent a function.
To determine the domain and range of the relation, we need to look at the x-values (inputs) and y-values (outputs) of the given pairs.
The x-values in the relation are: 6, -5, 9, 6
The y-values in the relation are: 2, 2, 7, 12
Domain: The domain is the set of all x-values in the relation. The unique x-values in the given pairs are 6, -5, and 9. Therefore, the domain of this relation is {-5, 6, 9}.
Range: The range is the set of all y-values in the relation. The unique y-values in the given pairs are 2, 7, and 12. Therefore, the range of this relation is {2, 7, 12}.
Now, let's determine whether the relation represents a function.
A relation represents a function if each input (x-value) has a unique output (y-value). In other words, each x-value cannot have more than one corresponding y-value.
In the given relation, we have two pairs with the same x-value, (6,2) and (6,12). This means that the x-value 6 is associated with two different y-values, 2 and 12. Therefore, the relation does not represent a function.
To summarize:
- Domain: {-5, 6, 9}
- Range: {2, 7, 12}
- The relation does not represent a function.
Well... it DOES NOT pass the straight line test. To be a function there can only be ONE y value for each x value. But clearly y is both 2 and 12 when x = 6.
But it is only 4 dots...
So.. .the domain starts at -5 and only goes to 9, that is
domain = {x| x = -5,6, 9}
Now you find the range