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Chapter 8--Transformations

Essential Question:  How do transformations of a function affect its equation, graph, or table of values?

Unit Rationale:  Transformations connect the study of functions to real-world situations such as computer graphics and animation.  Understanding transformations of functions helps us model situations in which a component has changed, such as a change in starting location, change in speed, etc.

As a result of this unit, students will be able to:

Ø  Describe and apply four ways of transforming a function or a figure-translating, reflecting, stretching/shrinking, and rotating, through graphs, words, symbols, and equations.

Ø  Write an equation that represents graphical transformation of a parent function (linear, absolute value, or quadratic).


·        Asymptote

·        Family of functions

·        Parabola

·        Parent function

·        Rational function

·        Rational expression

·        Reflect

·        Rotation

·        Shrink

·        Stretch

·        Transformations

·        Translate

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

*A1.4.E  Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationship they represent.

Supporting Standards:

A1.5.B  Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.

*A1.6.C  Describe how linear transformations affect the center and spread of univariate data.

Reasoning, Problem Solving, and Communication Standards:

A1.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.

A1.8.F  Summarize mathematical ideas with precision and efficiency for a given audience and purpose.