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 range 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 a relation is the set of all possible input values, or the set of values for the first components of the ordered pairs.
The range is the set of all possible output values, or the set of values for the second components of the ordered pairs.
In this case, the domain is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto} because these are the names of the planets listed.
The range is {14, 16, 46, 37} because these are the values associated with the planets.
To determine if the relation is a function, we need to check if there are any repeated first components (planet names) with different second components (values).
In this case, the relation is a function because each planet name is paired with a unique value. There are no repeated planet names with different values associated with them.
To find the domain and range of the relation, we need to consider the set of input values (domain) and the set of output values (range).
Domain: The domain is the set of all input values (in this case, the planets). So, the domain of this relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
Range: The range is the set of all output values. Looking at the given relation listed, we can see that the output values range from 14 to 46, with an additional value of 37. So, the correct range is {14, 16, 46, 37}.
Function: To determine if the relation is a function, we need to check if each input value (planet) is associated with a unique output value. If there are any repeated input values with different output values, then the relation is not a function.
In this case, we can see that both Venus and Neptune are associated with the output value of 14. Therefore, the relation is NOT a function.
So, the correct answer is (Venus, Mars, Jupiter, Saturn, Neptune, Pluto) as the domain and {14, 16, 46, 37} as the range.
To find the domain and range of a relation, we need to examine the given pairs and identify the unique values in the first (domain) column and the second (range) column.
Domain: The domain of a relation is the set of all unique values in the first column. Looking at the given pairs, the unique values in the first column are: Venus, Mars, Jupiter, Saturn, Neptune, Pluto.
Range: The range of a relation is the set of all unique values in the second column. Looking at the given pairs, the unique values in the second column are: 14, 16, 46, 37.
So the domain of the given relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto} and the range is {14, 16, 46, 37}.
To determine if the relation is a function, we need to check if each input (value in the domain) maps to a unique output (value in the range). If there are any cases where an input maps to multiple outputs, then the relation is not a function.
Looking at the given pairs, we can see that the input Venus maps to the output 14, and Neptune also maps to 14. Similarly, Mars and Jupiter both map to 16. Since there are multiple inputs that map to the same outputs, we can conclude that the given relation is not a function.
Therefore, the correct range is {14, 16, 46, 37} (Option O {14, 16, 46, 37}).