A relation is a pairing of x and y values. Domain can be defined as all of the x-values in a given relation. Range can be defined as all of the y-values of a relation.
Consider the relation given by the set of ordered pairs: \((-2, -3),\ (-1, 1),\ (1, 3),\ (2, -2),\ (3, 1)\). When you list the domain and range, the numbers need to be listed from least to greatest. The domain of the relation is \(\{-2, -1, 1, 2, 3\}\). The range of the relation is \(\{-3, -2, 1, 3\}\). When you have an x or y value that appears more than once, you only need to list the value once.
Consider the relation given by the set of ordered pairs: \((-2, -3),\ (-1, 1),\ (1, 3),\ (2, -2),\ (3, 1)\). When you list the domain and range, the numbers need to be listed from least to greatest. The domain of the relation is \(\{-2, -1, 1, 2, 3\}\). The range of the relation is \(\{-3, -2, 1, 3\}\). When you have an x or y value that appears more than once, you only need to list the value once.
Here is a list of other commonly used terms that can be used in place of domain and range:
Domain: x-value, input, independent variable
Range: y-value, output, dependent variable
A relation can be represented in multiple ways. Five ways to represent relations are using ordered pairs, tables, graphs, rules, and in contextual situations.
Example 1:
Given the following contextual situation, write the relation using each of the representations.
Context
You are thinking about treating \(5\) of your friends to some ice cream sandwiches down at the Snack Shack. Each ice cream sandwich costs \(\$2.00\). The number of friends represents the independent variable. The total cost represents the dependent variable.
Domain: x-value, input, independent variable
Range: y-value, output, dependent variable
A relation can be represented in multiple ways. Five ways to represent relations are using ordered pairs, tables, graphs, rules, and in contextual situations.
Example 1:
Given the following contextual situation, write the relation using each of the representations.
Context
You are thinking about treating \(5\) of your friends to some ice cream sandwiches down at the Snack Shack. Each ice cream sandwich costs \(\$2.00\). The number of friends represents the independent variable. The total cost represents the dependent variable.
Table
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Ordered Pairs
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Graph
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Rule (Equation)
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Quick Check
Given the following situation, represent the relation using ordered pairs, a graph, a table, and a rule.
Your little sister is thinking about making rubber band bracelets for you and three of your friends. The cost of materials for each bracelet is $1.50. How much will it cost if she decides to make the bracelets?
Quick Check Solutions
Given the following situation, represent the relation using ordered pairs, a graph, a table, and a rule.
Your little sister is thinking about making rubber band bracelets for you and three of your friends. The cost of materials for each bracelet is $1.50. How much will it cost if she decides to make the bracelets?
Quick Check Solutions