Problem 1 - Introductory Algebra for College Students

Question

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,2),(3,4),(5,5)\\}$$

Step-by-Step Solution

Answer

The given relation is indeed a function, because each element in the domain (the set {1, 3, 5}) maps to one and only one element in the range, which is the set {2, 4, 5}.

Step 1: Determine if it's a function

In the given relation, {(1,2),(3,4),(5,5)}, each input value (1,3 and 5) is paired to exactly one output value (2, 4 and 5 respectively). There are no repetitions of input values with different outputs. Therefore, given relation is indeed a function.

Step 2: Find the domain

The domain of a function is the set of all possible input values (also known as 'x' values) which will make the function work and will output real numbers. In this case, the input values are 1, 3, and 5. Therefore, the domain is {1, 3, 5}.

Step 3: Find the range

The range of a function is the set of all possible output values (also known as 'y' values), which come out from the function after we have put the domain values in. In this case, the output values are 2, 4, and 5. Therefore, the range is {2, 4, 5}.