Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)

Verified step by step guidance

1. Step 1: Recall the definition of a function. A relation is a function if every input (x-value) is paired with exactly one output (y-value). Check the given relation: (1, 10), (2, 500), (13, π). Verify that no x-value is repeated.
2. Step 2: Identify the domain of the relation. The domain is the set of all x-values (inputs) in the relation. Extract the x-values from the given pairs: {1, 2, 13}.
3. Step 3: Identify the range of the relation. The range is the set of all y-values (outputs) in the relation. Extract the y-values from the given pairs: {10, 500, π}.
4. Step 4: Confirm whether the relation is a function. Since each x-value (1, 2, 13) is paired with exactly one unique y-value (10, 500, π), the relation satisfies the definition of a function.
5. Step 5: Summarize the findings. The relation is a function. The domain is {1, 2, 13}, and the range is {10, 500, π}.

Key Concepts

Function Definition

A function is a specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that for any given x-value, there can only be one corresponding y-value. Understanding this definition is crucial for determining whether the given relations qualify as functions.

Domain and Range

The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Identifying the domain and range helps in understanding the behavior of the function and its limitations. For the given relations, the domain consists of the first elements of each ordered pair, and the range consists of the second elements.

Ordered Pairs

Ordered pairs are pairs of numbers written in the form (x, y), where x is the first element and y is the second element. In the context of relations and functions, the order of these elements is significant, as it determines the mapping from inputs to outputs. Analyzing the ordered pairs provided in the question is essential for assessing whether the relation is a function.