# MA.8.F.1.1

Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.

### Clarifications

Clarification 1: Instruction includes referring to the input as the independent variable and the output as the dependent variable.

Clarification 2: Within this benchmark, it is the expectation to represent domain and range as a list of numbers or as an inequality.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Functions
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.F.1.AP.1a: Given a set of ordered pairs, a table or mapping diagram identify whether the relationship is a function.
MA.8.F.1.AP.1b: Given a set of ordered pairs, a table or mapping diagram identify the domain and range of the relation.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Which Sequences Are Functions?:

Students are asked to determine if each of two sequences is a function and to describe its domain, if it is a function.

Type: Formative Assessment

Recognizing Functions:

Students are asked to determine whether or not each of two graphs represent functions.

Type: Formative Assessment

What Is a Function?:

Students are asked to define the term function and describe any important properties of functions.

Type: Formative Assessment

Car Wash:

Students are asked to describe the domain of a function given its graph.

Type: Formative Assessment

Circles and Functions:

Students are shown the graph of a circle and asked to identify a portion of the graph that could be removed so that the remaining portion represents a function.

Type: Formative Assessment

Cafeteria Function:

Students are asked decide if one variable is a function of the other in the context of a real-world problem.

Type: Formative Assessment

Identifying Functions:

Students are asked to determine if relations given by tables and mapping diagrams are functions.

Type: Formative Assessment

Identifying the Graphs of Functions:

Students are given four graphs and asked to identify which represent functions and to justify their choices.

Type: Formative Assessment

What Is a Function?:

Students are asked to define the term function including important properties.

Type: Formative Assessment

Tabulating Functions:

Students are asked to determine whether or not tables of ordered pairs represent functions.

Type: Formative Assessment

Identifying Algebraic Functions:

Students are asked to determine if each of three equations represents a function. Although the task provides equations, in their explanations students can use other representations such as ordered pairs, tables of values or graphs.

Type: Formative Assessment

## Lesson Plan

Functions: Domain and Range:

Students will identify if a graph represents a function and determine domain and range of the graphs.

Type: Lesson Plan

## Original Student Tutorials

Functions, Functions Everywhere: Part 1:

What is a function? Where do we see functions in real life? Explore these questions and more using different contexts in this interactive tutorial.

This is part 1 in a two-part series on functions. Click HERE to open Part 2.

Type: Original Student Tutorial

Driven By Functions:

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

Type: Original Student Tutorial

## Tutorials

Dependent and Independent Variables Exercise:

In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.

Type: Tutorial

Vertical Line Test:

A graph in Cartesian coordinates may represent a function or may only represent a binary relation. The "vertical line test" is a visual way to determine whether or not a graph represents a function.

Type: Tutorial

## Video/Audio/Animations

Real-Valued Functions of a Real Variable:

Although the domain and codomain of functions can consist of any type of objects, the most common functions encountered in Algebra are real-valued functions of a real variable, whose domain and codomain are the set of real numbers, R.

Type: Video/Audio/Animation

Domain and Range of Binary Relations:

Two sets which are often of primary interest when studying binary relations are the domain and range of the relation.

Type: Video/Audio/Animation

## MFAS Formative Assessments

Cafeteria Function:

Students are asked decide if one variable is a function of the other in the context of a real-world problem.

Car Wash:

Students are asked to describe the domain of a function given its graph.

Circles and Functions:

Students are shown the graph of a circle and asked to identify a portion of the graph that could be removed so that the remaining portion represents a function.

Identifying Algebraic Functions:

Students are asked to determine if each of three equations represents a function. Although the task provides equations, in their explanations students can use other representations such as ordered pairs, tables of values or graphs.

Identifying Functions:

Students are asked to determine if relations given by tables and mapping diagrams are functions.

Identifying the Graphs of Functions:

Students are given four graphs and asked to identify which represent functions and to justify their choices.

Recognizing Functions:

Students are asked to determine whether or not each of two graphs represent functions.

Tabulating Functions:

Students are asked to determine whether or not tables of ordered pairs represent functions.

What Is a Function?:

Students are asked to define the term function including important properties.

What Is a Function?:

Students are asked to define the term function and describe any important properties of functions.

Which Sequences Are Functions?:

Students are asked to determine if each of two sequences is a function and to describe its domain, if it is a function.

## Original Student Tutorials Mathematics - Grades 6-8

Driven By Functions:

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

## Original Student Tutorials Mathematics - Grades 9-12

Functions, Functions Everywhere: Part 1:

What is a function? Where do we see functions in real life? Explore these questions and more using different contexts in this interactive tutorial.

This is part 1 in a two-part series on functions. Click HERE to open Part 2.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Functions, Functions Everywhere: Part 1:

What is a function? Where do we see functions in real life? Explore these questions and more using different contexts in this interactive tutorial.

This is part 1 in a two-part series on functions. Click HERE to open Part 2.

Type: Original Student Tutorial

Driven By Functions:

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

Type: Original Student Tutorial

## Tutorials

Dependent and Independent Variables Exercise:

In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.

Type: Tutorial

Vertical Line Test:

A graph in Cartesian coordinates may represent a function or may only represent a binary relation. The "vertical line test" is a visual way to determine whether or not a graph represents a function.

Type: Tutorial

## Video/Audio/Animations

Real-Valued Functions of a Real Variable:

Although the domain and codomain of functions can consist of any type of objects, the most common functions encountered in Algebra are real-valued functions of a real variable, whose domain and codomain are the set of real numbers, R.

Type: Video/Audio/Animation

Domain and Range of Binary Relations:

Two sets which are often of primary interest when studying binary relations are the domain and range of the relation.

Type: Video/Audio/Animation

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.