Find the domain and range of the relation \( R = \{ (x, y) | y = 2x + 3 \} \).
Answer
The range of a relation is the set of all possible values of \( y \). Since \( y \) is dependent on \( x \) and \( x \) can take any real value, \( y \) can also take any real value. Therefore, the range is also all real numbers, denoted as \( R \).
Step 1 ：The given relation is \( y = 2x + 3 \).
Step 2 ：The domain of a relation is the set of all possible values of \( x \). Since \( x \) can be any real number in the given relation, the domain is all real numbers, denoted as \( R \).
Step 3 ：The range of a relation is the set of all possible values of \( y \). Since \( y \) is dependent on \( x \) and \( x \) can take any real value, \( y \) can also take any real value. Therefore, the range is also all real numbers, denoted as \( R \).
