Find the domain and the range of the following relation. Also determine whether the relation is a function.
Input:
Output:
Planet
Number of Solar
Congress Representatives
Venus
13
Mars
Jupiter
Saturn
Neptune
Pluto
30
35
21
The domain of the relation is the set of inputs, which in this case is the set of planets: Venus, Mars, Jupiter, Saturn, Neptune, Pluto.
The range of the relation is the set of outputs, which in this case is the set of numbers representing the number of solar congress representatives: 13, 30, 35, 21.
To determine whether the relation is a function, we need to check if each input (planet) is associated with exactly one output (number of solar congress representatives). In this case, all the planets are associated with a unique number of solar congress representatives, so the relation is indeed a function.
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Part 1
Find the domain and the range of the relation. Determine whether the relation is a function.
Input
Output
-5
3
-9
9
30
The domain of the relation is the set of inputs, which in this case is {-5, -9, 9}.
The range of the relation is the set of outputs, which in this case is {3, 30}.
To determine whether the relation is a function, we need to check if each input is associated with exactly one output. In this case, the input -5 is associated with the output 3, -9 is associated with 30, and 9 is also associated with 30. Therefore, the relation is not a function since the input 9 is associated with two different outputs.
To find the domain and range of the given relation, we need to identify the set of all possible inputs (domain) and the corresponding set of outputs (range).
In this case, the inputs are planets: Venus, Mars, Jupiter, Saturn, Neptune, and Pluto. Therefore, the domain of the relation is {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}.
The outputs are the number of Congress representatives for each planet: 13, 30, 35, and 21. So, the range of the relation is {13, 30, 35, 21}.
To determine whether the relation is a function, we need to check if each input (planet) is associated with exactly one output (number of Congress representatives). A relation is considered a function if each element in the domain has a unique corresponding element in the range.
In this case, there are no repetitions in the planets, and each planet is associated with exactly one number of Congress representatives. Therefore, this relation is a function.
To summarize:
Domain: {Venus, Mars, Jupiter, Saturn, Neptune, Pluto}
Range: {13, 30, 35, 21}
Relation: Function