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
Is the relation a function?
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 the first elements in each ordered pair, which are the names of the planets: {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
The range of the relation is the set of all the second elements in each ordered pair, which are the given numbers: {14, 16, 46, 14, 37}.
To determine whether the relation is a function, we must check if there are any repeated first elements (planets) with different second elements (numbers).
In this case, both Mars and Jupiter have the same second element (16), which means that the relation is not a function.
Therefore, the answer is: None of the above.
To find the domain and range of the relation, we need to look at the first and second values of each ordered pair:
Domain: The domain is the set of all possible input values, which in this case, are the first values of the ordered pairs. So the domain for this relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
Range: The range is the set of all possible output values, which in this case, are the second values of the ordered pairs. So the range for this relation is {14, 16, 46, 37}.
To determine if the relation is a function, we need to check if there is more than one output value for the same input value. In this case, each planet (input value) has only one associated number (output value), so the relation is a function.
Therefore, the correct answer is:
- The domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).
- The range is {14, 16, 46, 37}.
- The relation is a function.
- The answer is option O (Venus, Mars, Jupiter, Saturn, Neptune, Pluto).
To find the domain and the range of a relation, we need to look at the set of input values (domain) and the corresponding set of output values (range).
In this case, the domain would be the set of all planets mentioned in the relation, which are:
Domain: {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}
The range would be the set of all numbers listed in the relation. Since there are duplicate numbers, we only include distinct values:
Range: {14, 16, 46, 37}
To determine whether the relation is a function, we need to check if each input (planet) is associated with exactly one output value.
Looking at the given relation, we find that:
- Venus is associated with 14
- Mars is associated with 16
- Jupiter is associated with 16
- Saturn is associated with 46
- Neptune is associated with 14
- Pluto is associated with 37
Since each planet is associated with only one output, the relation is indeed a function.
Therefore, the answer is:
The domain is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto) and the range is {14, 16, 46, 37}. The relation is a function.