# Standard 1: Define, evaluate and compare functions.

General Information
Number: MA.8.F.1
Title: Define, evaluate and compare functions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Functions

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

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.
MA.8.F.1.AP.2
Given a function displayed as a graph or an equation, identify whether the function is a linear function.
MA.8.F.1.AP.3

Given a functional relationship displayed as a graph, identify where the function is increasing, decreasing, or constant.

## Related Resources

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

## Formative Assessments

Population Trend:

Students are asked to describe the relationship between two quantities in a nonlinear function.

Type: Formative Assessment

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

Jet Fuel:

Students are asked to analyze and describe the relationship between two linearly related quantities.

Type: Formative Assessment

Graph the Ride:

Students are given a verbal description of the relationship between two quantities and are asked to sketch a graph to model the relationship.

Type: Formative Assessment

Bacterial Growth Graph:

Students are given a verbal description of the relationship between two quantities and are asked to sketch a graph to model the relationship.

Type: Formative Assessment

Recognizing Functions:

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

Type: Formative Assessment

What Am I?:

Students are asked to describe a linear function, its graph, and the meaning of its parameters.

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

Linear or Nonlinear?:

Students are asked to identify a function as either linear or nonlinear and to justify their decision.

Type: Formative Assessment

Explaining Linear Functions:

Students are asked to describe defining properties of linear functions.

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

Taxi Ride:

Students are asked to sketch a graph from a verbal description.

Type: Formative Assessment

Bike Race:

Students are asked to evaluate three verbal descriptions and to state why each does or does not match a given graph.

Type: Formative Assessment

## Lesson Plans

Functions: Domain and Range:

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

Type: Lesson Plan

Functions: Are They Linear or Non-Linear?:

In this lesson, students will investigate 5 different functions to see if they are linear or non-linear. They will then analyze the functions in groups. After that they will present their results and reasoning.

Type: Lesson Plan

Constructing and Calibrating a Hydrometer:

Students construct and calibrate a simple hydrometer using different salt solutions. They then graph their data and determine the density and salinity of an unknown solution using their hydrometer and graphical analysis.

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

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Cruising Through Functions:

Cruise along as you discover how to qualitatively describe functions in this interactive tutorial.

Type: Original Student Tutorial

Summer of FUNctions:

Have some fun with FUNctions! Learn how to identify linear and non-linear functions in this interactive tutorial.

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

## Perspectives Video: Expert

Using Mathematics to Optimize Wing Design:

Nick Moore discusses his research behind optimizing wing design using inspiration from animals and how they swim and fly.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Asymptotic Behavior in Shark Growth Research:

Fishery Scientist from Florida State University discusses his new research in deep sea sharks and the unusual behavior that is found when the data is graphed.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Kites, Wind, and Speed:

Lofty ideas about kites helped power a kayak from California to Hawaii.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## 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

## Virtual Manipulative

Functions and Vertical Line Test:

This lesson is designed to introduce students to the vertical line test for functions as well as practice plotting points and drawing simple functions. The lesson provides links to discussions and activities related to the vertical line test and functions as well as suggested ways to integrate them into the lesson.

Type: Virtual Manipulative

## Student Resources

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

## 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

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Cruising Through Functions:

Cruise along as you discover how to qualitatively describe functions in this interactive tutorial.

Type: Original Student Tutorial

Summer of FUNctions:

Have some fun with FUNctions! Learn how to identify linear and non-linear functions in this interactive tutorial.

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 topic.