Problem 9 - Precalculus Essentials

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,4),(1,5),(1,6)\\}$$

Step-by-Step Solution

Answer

The given relation is not a function. The domain of the relation is {1} and the range is {4,5,6}.

Step 1: Analyzing the given relation

The relation given is {(1,4),(1,5),(1,6)}. This can be broken down as the input 1 is related to outputs 4, 5, and 6. According to the definition of a function, each input should be related to exactly one output.

Step 2: Determining whether the relation is a function

Since the input 1 is related to more than one output (4, 5, and 6), this relation does not satisfy the condition for being a function. This means, it is not a function.

Step 3: Establishing the domain and range

The domain is the set of all possible input values and the range is the set of all possible output values for a function. Here, since only one value has been used as input (1), the domain of the relation is {1}. The range includes all the outputs, which in this case are 4, 5, and 6. Therefore, the range is the set {4,5,6}.