A1.F.1.1 Distinguish between relations and functions.
In a Nutshell
Students will understand functions as a wellbehaved subdomain of a relation. Relations are simply a mapping from a domain to a range while a function is a type of relationship in which each element of the domain is mapped to only one related element of the range.
Student Actions

Teacher Actions



Key Understandings

Misconceptions

 Build an understanding that a function comes from one element in the input (called the domain) being assigned exactly one element from the output (called the range) ..
Examples:
Graph A is only a relation since there are 2 ordered pairs with the same xvalue and a different yvalues at numerous places on the graph.
Graph B is a relation which is also a function.
Ordered pairs can be in a table or in a set list. This table is a relation that is a function, since each xvalue is assigned to only one y value f(x).
x

f(x)

2

5

0

7

2

12

4

16

This table is only a relation and not a function since the xvalue 2 has two different values assigned to it.


Students mistake a vertical line for a horizontal line when investigating the characteristics of the functions.

Students don’t realize a function is a special relation.

Students interchange the domain values and range values when interpreting a function.

OKMath Framework Introduction
Algebra 1 Introduction
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