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

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

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

Parent Resources

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