What is a Relation in Math? Definition & Examples for Algebra 1

📚 Quick Study Guide

🔢 A relation is a set of ordered pairs. Think of it as a way to show a connection between two things. 📍 The set of all first elements (x-values) in the ordered pairs is called the domain. 📐 The set of all second elements (y-values) in the ordered pairs is called the range. 📈 Relations can be represented in several ways: as a set of ordered pairs, a table, a graph, a mapping diagram, or an equation. 💡 Not all relations are functions. For a relation to be a function, each element in the domain must be paired with only one element in the range. 📝 Example: The relation {(1, 2), (3, 4), (5, 6)} has a domain of {1, 3, 5} and a range of {2, 4, 6}.

Practice Quiz

1. Which of the following is a relation?
   1. A) $y = 2x + 1$
   2. B) {(1, 5), (2, 6), (3, 7)}
   3. C) A line on a graph
   4. D) All of the above
2. What is the domain of the relation {(0, 1), (2, 3), (4, 5)}?
   1. A) {1, 3, 5}
   2. B) {0, 2, 4}
   3. C) {0, 1, 2, 3, 4, 5}
   4. D) {0, 3, 5}
3. What is the range of the relation {(−1, 2), (0, 0), (1, 2)}?
   1. A) {−1, 0, 1}
   2. B) {0, 2}
   3. C) {−1, 0, 1, 2}
   4. D) {2}
4. Which representation is NOT typically used to show a relation?
   1. A) Equation
   2. B) Graph
   3. C) Novel
   4. D) Table
5. Given the relation {(2, a), (3, b), (4, a)}, what are the domain and range?
   1. A) Domain: {a, b}, Range: {2, 3, 4}
   2. B) Domain: {2, 3, 4}, Range: {a, b}
   3. C) Domain: {2, 3, 4}, Range: {a}
   4. D) Domain: {a, b}, Range: {a}
6. Which of the following relations is a function?
   1. A) {(1, 2), (1, 3), (2, 4)}
   2. B) {(1, 2), (2, 2), (3, 2)}
   3. C) {(1, 2), (2, 3), (1, 4)}
   4. D) {(1, 2), (2, 3), (3, 2), (2, 1)}
7. If a mapping diagram shows multiple arrows leaving one element in the domain, the relation is:
   1. A) Always a function
   2. B) Never a function
   3. C) Sometimes a function
   4. D) Always a line