Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Assessed with:
MAFS.912.FIF.1.2
Related Courses
Related Access Points
Related Resources
Assessments
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Professional/Enthusiast
ProblemSolving Tasks
Professional Development
Tutorials
Unit/Lesson Sequence
Video/Audio/Animations
Virtual Manipulatives
MFAS Formative Assessments
Students are asked decide if one variable is a function of the other in the context of a realworld problem.
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.
Students are asked to determine if relations given by tables and mapping diagrams are functions.
Students are given four graphs and asked to identify which represent functions and to justify their choices.
Students are asked to define the term function and describe any important properties of functions.
Students are asked to create their own examples and nonexamples of functions by completing tables and mapping diagrams.
Original Student Tutorials Mathematics  Grades 912
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 twopart series on functions. Click HERE to open Part 2 (Coming Soon).
Continue exploring how to determine if a relation is a function using graphs and story situations, in this interactive tutorial. This is Part 2 of a 2 part tutorial series.
Student Resources
Original Student Tutorials
Continue exploring how to determine if a relation is a function using graphs and story situations, in this interactive tutorial. This is Part 2 of a 2 part tutorial series.
Type: Original Student Tutorial
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 twopart series on functions. Click HERE to open Part 2 (Coming Soon).
Type: Original Student Tutorial
ProblemSolving Tasks
This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.
Type: ProblemSolving Task
This task addresses a common misconception about function notation.
Type: ProblemSolving Task
The purpose of this task is to investigate the meaning of the definition of function in a realworld context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
Type: ProblemSolving Task
The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).
Type: ProblemSolving Task
The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant reallife context.
Type: ProblemSolving Task
This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
Type: ProblemSolving Task
This problem is a simple decontextualized version of FIF Your Father and FIF Parking Lot. It also provides a natural context where the absolute value function arises as, in part (b), solving for x in terms of y means taking the square root of x^2 which is x.This task assumes students have an understanding of the relationship between functions and equations.
Type: ProblemSolving Task
The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.
Type: ProblemSolving Task
Tutorials
This tutorial will help the students to understand the function notation such as f(x), which can be thought as another way of representing the yvalue in a function, especially when graphing. The yaxis is even labeled as the f(x) axis, when graphing.
Type: Tutorial
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
This video will demonstrate how to determine what is and is not a function.
Type: Video/Audio/Animation
Although the domain and codomain of functions can consist of any type of objects, the most common functions encountered in Algebra are realvalued functions of a real variable, whose domain and codomain are the set of real numbers, R.
Type: Video/Audio/Animation
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
In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
Parent Resources
ProblemSolving Tasks
This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.
Type: ProblemSolving Task
This task addresses a common misconception about function notation.
Type: ProblemSolving Task
The purpose of this task is to investigate the meaning of the definition of function in a realworld context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
Type: ProblemSolving Task
The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).
Type: ProblemSolving Task
The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant reallife context.
Type: ProblemSolving Task
This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
Type: ProblemSolving Task
This problem is a simple decontextualized version of FIF Your Father and FIF Parking Lot. It also provides a natural context where the absolute value function arises as, in part (b), solving for x in terms of y means taking the square root of x^2 which is x.This task assumes students have an understanding of the relationship between functions and equations.
Type: ProblemSolving Task
The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.
Type: ProblemSolving Task