Relations & Linear Functions
Definition 1: A relation is a set of ordered pairs where the first components of the ordered pairs are the input values and the second components are the output values.
Definition 2: A function is a relation that assigns to each input number EXACTLY ONE output number.
Definition 3: The domain is the set of all input values to which the rule applies. These are called the independent variables. These are the values that correspond to the first components of the ordered pairs it is associated with.
Definition 4: The range is the set of all output values. These are called your dependent variables. These are the values that correspond to the second components of the ordered pairs it is associated with.
Example 1: Find the domain and range of the relation. Determine whether the relation is a function: {(-2, 2), (5, 3), (-6, 4), (1, 10)}
Domain is the set of all input values. In terms of ordered pairs, it is the first component of each one. Therefore, the domain is {-2, 5, -6, 1}
Range is the set of all output values. In terms of ordered pairs, it is the second component of each one. Therefore, the range is {2, 3, 4, 10}
To determine if the given relation is a function, we have to check if every first element (or input) corresponds to exactly one second element (or output). For {(-2, 2), (5, 3), (-6, 4), (1, 10)}: -2 goes only to 2, 5 goes only to 3, -6 goes only to 4, 1 goes only to 10.
Therefore, the relation is a function.
To find out more about relations and linear functions, read the explanation below.
Practice: Answer the following exercises about relations and linear functions.