Question

name makaylah
date 11/26/2025
period 6
relations & functions - functions guided notes
lesson objectives ·students will create and interpret mapping diagrams.
·students will determine if relations are functions.
essential question - what strategies can you use to determine if a relation is a function?
vocabulary term | definition
(x, y) | input
| output
| ordered pair
relation
definition →
ordered pairs | table | mapping diagram

Answer:

To answer the vocabulary definitions for the given worksheet (related to functions in mathematics):

For the \((x, y)\) - related vocabulary:

• Input: In a function or relation, the input is the value (usually the \(x\) - value in an \((x,y)\) ordered pair) that is used as the independent variable. It is the value that we put into a rule or a relation to get an output.
• Output: In a function or relation, the output is the value (usually the \(y\) - value in an \((x,y)\) ordered pair) that is the result of applying a rule or a relation to the input. It is the dependent variable, as its value depends on the input.
• Ordered Pair: An ordered pair \((x,y)\) is a pair of numbers (or other mathematical objects) where the order of the elements matters. In the context of functions and relations, the first element (usually \(x\)) is the input - related value and the second element (usually \(y\)) is the output - related value. It is used to represent a point in a coordinate plane or to represent the mapping from an input to an output in a relation.

For the "Relation" section:

• Definition of Relation: A relation is a set of ordered pairs, or a rule that describes a relationship between two sets (usually a set of inputs and a set of outputs). It can be represented in different ways such as ordered pairs, tables, or mapping diagrams. It shows how elements from one set (the domain) are related to elements from another set (the range).

For the different representations of a relation:

• Ordered Pairs: As defined above, a relation represented by ordered pairs is a collection of \((x,y)\) pairs where each \(x\) (from the domain) is related to a \(y\) (from the range). For example, \(\{(1,2),(3,4),(5,6)\}\) is a relation represented by ordered pairs.
• Table: A table representation of a relation lists the input values (usually in one column) and the corresponding output values (in another column). For example, if we have a table with \(x\) values \(1,3,5\) in one column and \(y\) values \(2,4,6\) in the next column, this table represents the same relation as the ordered - pair example above.
• Mapping Diagram: A mapping diagram for a relation has two sets of ovals (or other shapes). One set represents the domain (input values) and the other represents the range (output values). Arrows are drawn from elements in the domain oval to the corresponding elements in the range oval to show the relationship between the input and output values. For example, if the domain is \(\{1,3,5\}\) and the range is \(\{2,4,6\}\), we draw an arrow from \(1\) to \(2\), from \(3\) to \(4\), and from \(5\) to \(6\) to represent the relation.

If you were looking for filling the worksheet:

Vocabulary Term	Definition
\((x,y)\) - Output	The value (usually \(y\)) resulting from applying a relation/function to an input
\((x,y)\) - Ordered Pair	A pair \((x,y)\) where order (x first, y second) matters, representing input - output or a coordinate
Relation - Definition	A set of ordered pairs (or rule) relating two sets (domain & range)
Relation - Ordered Pairs	A relation shown as \((x_1,y_1),(x_2,y_2),\dots\)
Relation - Table	A relation shown with input (e.g., \(x\)) and output (e.g., \(y\)) columns
Relation - Mapping Diagram	A relation shown with domain (input) and range (output) sets, connected by arrows

If you have a specific part of the worksheet (like a particular vocabulary or representation) that you want more details on, please let me know!