Find the domain and the range of the following relation. Also determine whether the relation is a function.
Venus 15
Mars
Jupiter 48
Saturn 50
Neptune
Pluto 34
The given relation includes the following pairs:
Venus 15
Mars
Jupiter 48
Saturn 50
Neptune
Pluto 34
The domain of a relation is the set of all the inputs (or x-values) in the relation. In this case, the inputs are the planets. So, the domain of this relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
The range of a relation is the set of all the outputs (or y-values) in the relation. In this case, the outputs are the numbers associated with each planet. So, the range of this relation is {15, 48, 50, 34}.
To determine if the relation is a function, we need to check if each input (planet) is associated with exactly one output (number). In this case, Venus is associated with 15, Jupiter is associated with 48, Saturn is associated with 50, and Pluto is associated with 34. However, Mars and Neptune are not associated with any number.
Since Mars and Neptune are not associated with any number, the relation is not a function.