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 No
O yes
To find the domain and range of the given relation, we can start by listing all the inputs (the domain) and outputs (the range) of the relation:
Domain: Venus, Mars, Jupiter, Saturn, Neptune, Pluto
Range: 14, 16, 46, 37
Therefore, the domain of the relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto} and the range is {14, 16, 46, 37}.
To determine whether the relation is a function, we need to check if each input has one and only one corresponding output. Looking at the given data, there are no repeated inputs, and each input has a unique output. Therefore, the relation is a function.
Thus, the relation is a function and the answer is "yes".
To find the domain and range of a relation, we need to examine the input values (domain) and the output values (range) of the relation.
In this case, the given relation consists of pairs of planets and numbers. The planets are the input values (domain) and the corresponding numbers are the output values (range).
Domain: The domain of the relation is all the possible input values, which are the names of the planets mentioned in the list: Venus, Mars, Jupiter, Saturn, Neptune, and Pluto.
Range: The range of the relation is all the possible output values, which are the numbers associated with each planet in the list: 14, 16, 46, and 37.
Now, let's determine whether the relation is a function. A relation is considered a function if each input value has only one corresponding output value.
Looking at the given relation, we can see that each planet has a unique number associated with it, and there are no repetitions. Therefore, every input (planet) has only one output (number), which means that the relation is a function.
To summarize:
Domain: {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}
Range: {14, 16, 46, 37}
The relation is a function: Yes
The domain of the relation is the set of all input values. In this case, the input values are the names of the planets: Venus, Mars, Jupiter, Saturn, Neptune, and Pluto.
The range of the relation is the set of all output values. In this case, the output values are the numbers: 14, 16, 46, and 37.
To determine whether the relation is a function, we need to check if each input (planet) is associated with only one output (number). Looking at the given information, we can see that both Mars and Jupiter are associated with the number 16, so the relation is not a function.
Therefore, the relation is not a function, and the correct answer is: No.