Unit 6: Transformations of Functions

Students examine how functions can be transformed by translations, reflections, and scaling of inputs and outputs, generalize even and odd symmetry, and apply transformations to model real-world data.

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Concept

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What this unit covers

A Translations, Reflections, and Symmetry · 7 lessons

Goals

• Create equations to represent known translations and reflections of a graph.
• Justify why a function is even, odd, or neither from an equation.
• Use function notation to represent a transformation from one graph to another.

Lessons

1. Matching Up to Data
2. Moving Functions
3. More Movement
4. Reflecting Functions
5. Some Functions Have Symmetry
6. Symmetry in Equations
7. Expressing Transformations of Functions Algebraically

B Scaling Outputs and Inputs · 3 lessons

Goals

• Calculate the scale factor needed to transform the input or output of a function to fit data.
• Create new functions by adding, subtracting, multiplying, and dividing functions.

Lessons

1. Scaling the Outputs
2. Scaling the Inputs
3. Combining Functions

C Transformations of Functions · 4 lessons

Goals

• Create a graph of a function given an original function and a transformation.
• Create an equation for a function that has been transformed from a specific function and an unknown function f.

Lessons

1. Transforming from an Original Function
2. Transformation Effects
3. Transforming Parabolas
4. Transforming Circles (Optional)

D Let’s Put It to Work · 1 lesson

Lessons

1. Making a Model for Data