Given the set of ordered pair, find the domain and range, graph using mapping diagram and tell whether each set is a function or not
a) {(2,3), (2,4),(5,6),(7,8),(0,1)}
b) {(2,3),(3,2),(4,5),(5,4),(6,7),(7,6)}
c) {(4,3),(2,3),(1,3),(3,3),(5,3)}
d) {(1,2),(1,4),(1,3),(1,5),(1,6),(1,1)}?
for each set of (x,y) pairs,
domain is the set of all x values
range is the set of all y values
If no x value is used more than once, it is a function -- otherwise, not
I am not going to do all this for you but immediately
a) not a function, when x = 2 we have two values of y
b) looks ok but note goes up then down
c) horizontal line, range kind of limited
d) vertical line, domain is x= 1
To find the domain and range of a set of ordered pairs, you need to identify all the unique x-values (for the domain) and the unique y-values (for the range).
Let's go through each set of ordered pairs and determine their domain and range, graph them using a mapping diagram, and determine if each set is a function or not.
a) {(2,3), (2,4), (5,6), (7,8), (0,1)}
- Domain: The unique x-values in the set are 2, 5, 7, and 0. So, the domain is {2, 5, 7, 0}.
- Range: The unique y-values in the set are 3, 4, 6, 8, and 1. So, the range is {3, 4, 6, 8, 1}.
- Mapping Diagram:
2 --> (3, 4)
5 --> (6)
7 --> (8)
0 --> (1)
Here, the arrow from each x-value to corresponding y-value represents the mapping relationship.
- Is it a function? No, because there are multiple ordered pairs with the same x-value but different y-values.
b) {(2,3), (3,2), (4,5), (5,4), (6,7), (7,6)}
- Domain: The unique x-values in the set are 2, 3, 4, 5, 6, and 7. So, the domain is {2, 3, 4, 5, 6, 7}.
- Range: The unique y-values in the set are 3, 2, 5, 4, 7, and 6. So, the range is {3, 2, 5, 4, 7, 6}.
- Mapping Diagram:
2 --> (3)
3 --> (2)
4 --> (5)
5 --> (4)
6 --> (7)
7 --> (6)
Here, each x-value corresponds to a unique y-value.
- Is it a function? Yes, because each x-value has a unique y-value associated with it.
c) {(4,3), (2,3), (1,3), (3,3), (5,3)}
- Domain: The unique x-values in the set are 4, 2, 1, and 3. So, the domain is {4, 2, 1, 3}.
- Range: The unique y-value in the set is 3. So, the range is {3}.
- Mapping Diagram:
4 --> (3)
2 --> (3)
1 --> (3)
3 --> (3)
5 --> (3)
Here, each x-value corresponds to the same y-value.
- Is it a function? Yes, because each x-value has the same y-value associated with it.
d) {(1,2), (1,4), (1,3), (1,5), (1,6), (1,1)}
- Domain: The unique x-values in the set is 1. So, the domain is {1}.
- Range: The unique y-values in the set are 2, 4, 3, 5, 6, and 1. So, the range is {2, 4, 3, 5, 6, 1}.
- Mapping Diagram:
1 --> (2, 4, 3, 5, 6, 1)
Here, the arrow represents multiple y-values corresponding to a single x-value.
- Is it a function? No, because there are multiple ordered pairs with the same x-value but different y-values.
In summary:
a) Not a function
b) Function
c) Function
d) Not a function