Standard 2: Identify and describe the effects of transformations on functions. Create new functions given transformations.

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General Information
Number: MA.912.F.2
Title: Identify and describe the effects of transformations on functions. Create new functions given transformations.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Functions

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.F.2.AP.1

Select the effect (up, down, left, or right) on the graph of a given function after replacing f(x) by f(x) + k and f(x + k) for specific values of k.
MA.912.F.2.AP.2

Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values.
MA.912.F.2.AP.3

Given the graph of a given function after replacing f(x) by f(x) + k and f(x + k), kf(c), for specific values of k select the type of transformation and find the value of the real number k.
MA.912.F.2.AP.5
Given a table, equation or graph that represents a function, select a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values.

Related Resources

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

Formative Assessments

Comparing Functions – Quadratic:

Students are given the graph of f(x) = x2 and are asked to compare the graphs of five other quadratic functions to the graph of f.

Type: Formative Assessment

Write the Equations:

Students are given the graphs of three absolute values functions and are asked to write the equation of each.

Type: Formative Assessment

Comparing Functions - Linear:

Students are asked to compare the graphs of four different linear functions to the graph of f(x) = x.

Type: Formative Assessment

Lesson Plans

Transforming Quadratics - The basics:

This lesson introduces students to the quadratic parent function, as well as reinforces some key features of quadratic functions. It allows students to explore basic transformations of quadratic functions and provides a note-taking sheet for students to organize their learning. There is a "FUN" cut and paste activity for students to match quadratic graphs with verbal descriptions and their equations.

Type: Lesson Plan

Graphing Quadratics Made Easy: Vertex Form of the Equation:

This lesson covers quadratic translations as they relate to vertex form of a quadratic equation. Students will predict what will happen to the graph of a quadratic function when more than one constant is in a quadratic equation. Then, the students will graph quadratic equations in vertex form using their knowledge of the translations of a quadratic function, as well as describe the translations that occur. Students will also identify the parent function of any quadratic function as .

Type: Lesson Plan

Translating Quadratic Functions:

In this lesson, students will investigate the changes to the graph of a quadratic function when the function is modified in four different ways by inclusion of an additive or multiplicative constant. Students will work in groups to graph quadratic functions, prepare a display of their functions, and determine how the modification affects the graph of the quadratic function. Then, students participate in a gallery walk, where members of each group will share their findings with a small group of students. At the end, there is a class discussion to see if everyone had similar findings and to solidify the knowledge of translating quadratic functions.

Type: Lesson Plan

Graphing Quadratic Equations:

This is an introductory lesson to graphing quadratic equations. This lesson uses graphing technology to illustrate the differences between quadratic equations and linear equations. In addition, it allows students to identify important parts of the quadratic equation and how each piece changes the look of the graph.

Type: Lesson Plan

Graphing Quadratic Equations:

This is an introductory lesson to graphing quadratic equations. This lesson uses graphing technology to illustrate the differences between quadratic equations and linear equations. In addition, it allows students to identify important parts of the quadratic equation and how each piece changes the look of the graph.

Type: Lesson Plan

Original Student Tutorials

Dilations...The Effect of k on a Graph:

Visualize the effect of using a value of k in both kf(x) or f(kx) when k is greater than zero in this interactive tutorial.

Type: Original Student Tutorial

Reflections...The Effect of k on a Graph:

Learn how reflections of a function are created and tied to the value of k in the mapping of f(x) to -1f(x) in this interactive tutorial.

Type: Original Student Tutorial

Translations...The Effect of k on the Graph:

Explore translations of functions on a graph that are caused by k in this interactive tutorial. GeoGebra and interactive practice items are used to investigate linear, quadratic, and exponential functions and their graphs, and the effect of a translation on a table of values.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Absolute Value Progression:

Unlock an effective teaching strategy for making connections with absolute values to graphing in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Problem-Solving Task

Interpreting the Graph:

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: Problem-Solving Task

Student Resources

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

Original Student Tutorials

Dilations...The Effect of k on a Graph:

Visualize the effect of using a value of k in both kf(x) or f(kx) when k is greater than zero in this interactive tutorial.

Type: Original Student Tutorial

Reflections...The Effect of k on a Graph:

Learn how reflections of a function are created and tied to the value of k in the mapping of f(x) to -1f(x) in this interactive tutorial.

Type: Original Student Tutorial

Translations...The Effect of k on the Graph:

Explore translations of functions on a graph that are caused by k in this interactive tutorial. GeoGebra and interactive practice items are used to investigate linear, quadratic, and exponential functions and their graphs, and the effect of a translation on a table of values.

Type: Original Student Tutorial

Problem-Solving Task

Interpreting the Graph:

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: Problem-Solving Task

Parent Resources

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

Problem-Solving Task

Interpreting the Graph:

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: Problem-Solving Task