Find the domain and the range of the following relation. Also determine whether the relation is a function.
Venus 14
Mars 16
Jupiter 16
Saturn 46
Neptune 14
Pluto 37
Choose the correct domain below.
O 14 to 46
O {14, 16, 46, 37\}
O (Venus, Mars, Jupiter, Saturn, Neptune, Pluto) O None of the above
The domain of the relation is the set of all possible input values, which in this case is the set of all planets mentioned: {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
The range of the relation is the set of all possible output values, which in this case are the numbers given: {14, 16, 46, 37}.
To determine whether the relation is a function, we need to check if each input value (planet) is associated with exactly one output value (number).
In this case, Venus and Neptune are associated with the number 14, Mars and Jupiter are associated with the number 16, Saturn is associated with 46, and Pluto is associated with 37.
Since each input value is associated with exactly one output value, the relation is a function.
Therefore, the correct answer for the domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).
The domain of a relation refers to the set of all input values or elements from the first column of the relation. In this case, the domain would be "Venus, Mars, Jupiter, Saturn, Neptune, Pluto" since these are the values listed in the first column.
The range of a relation refers to the set of all output values or elements from the second column of the relation. In this case, the range would be "{14, 16, 46, 37}" since these are the values listed in the second column.
To determine if the relation is a function, we need to check if each input value (domain element) corresponds to a unique output value (range element). Looking at the relation:
Venus 14
Mars 16
Jupiter 16
Saturn 46
Neptune 14
Pluto 37
Both Venus and Neptune have the same output value of 14, which means the input 14 is associated with two different outputs. Therefore, the relation is not a function.
Therefore, the correct answer for the domain is: (Venus, Mars, Jupiter, Saturn, Neptune, Pluto)
To find the domain and range of the given relation, we need to consider the first column (Venus, Mars, Jupiter, Saturn, Neptune, Pluto) as the domain and the second column (14, 16, 16, 46, 14, 37) as the range.
Domain: The domain of a relation is the set of all possible inputs or x-values. In this case, the domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).
Range: The range of a relation is the set of all possible outputs or y-values. In this case, the range is {14, 16, 46, 37}.
Now, let's determine whether the relation is a function. A relation is considered a function if each input (x-value) is associated with a unique output (y-value). Looking at the relation, we can see that both Mars and Jupiter are associated with the same output value (16). Therefore, the relation is not a function.
In conclusion:
- The domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).
- The range is {14, 16, 46, 37}.
- The relation is not a function.
Therefore, the correct choice for the domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).