In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn to define relations and functions, represent them using ordered pairs and mapping diagrams, and determine whether a relation qualifies as a function by checking that each input is paired with exactly one output. Through activities involving area, perimeter, circumference, and volume, students practice constructing and interpreting mapping diagrams to describe relationships between two data sets.
Section 1
Introduction to Input-Output Relationships
In many real-world situations, there is a relationship between two quantities where one quantity (the input) determines the value of another quantity (the output). We can identify these input-output relationships by examining how changes in one variable correspond to changes in another variable.
Section 2
Relation, Domain, and Range
A relation is any set of ordered pairs, . All the -values in the ordered pairs together make up the domain. All the -values in the ordered pairs together make up the range.
A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.
Section 3
Spotting Functions in Tables and Mapping Diagrams
Relations can be represented in three equivalent forms: ordered pairs (x, y), tables, and mapping diagrams with arrows.
To be a function, every input must have exactly one arrow pointing away from it (in a diagram) or correspond to exactly one output (in a table). It is completely acceptable for different inputs to share the same output.
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Section 1
Introduction to Input-Output Relationships
In many real-world situations, there is a relationship between two quantities where one quantity (the input) determines the value of another quantity (the output). We can identify these input-output relationships by examining how changes in one variable correspond to changes in another variable.
Section 2
Relation, Domain, and Range
A relation is any set of ordered pairs, . All the -values in the ordered pairs together make up the domain. All the -values in the ordered pairs together make up the range.
A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.
Section 3
Spotting Functions in Tables and Mapping Diagrams
Relations can be represented in three equivalent forms: ordered pairs (x, y), tables, and mapping diagrams with arrows.
To be a function, every input must have exactly one arrow pointing away from it (in a diagram) or correspond to exactly one output (in a table). It is completely acceptable for different inputs to share the same output.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter