Section

Teacher-facing learning goals

Translations, Reflections, and Symmetry

Lesson 1

Lesson 2

Use function notation to represent a vertical or horizontal translation from one graph to another.

Lesson 3

Create an equation to represent the vertical and horizontal translations needed to move one graph to another.
Describe the effect on a graph by replacing \(f(x)\) with \(f(x)+k\) and \(f(x+k)\).

Lesson 4

Comprehend that "reflecting" a function's graph across an axis means replacing either the inputs or the outputs with their opposite values.
Create a graph of \(y=\text-f(x)\) or \(y=f(\text-x)\) given the graph of \(y=f(x)\).

Lesson 5

Generalize (orally and in writing) what is true for coordinate pairs of even and odd functions.
Identify (orally) features that graphs of even functions have in common and features that graphs of odd functions have in common.

Lesson 6

Explain (orally) how to sketch the second half of an even or odd function given the first half.
Justify (orally and in writing) why a function is even, odd, or neither from an equation.

Lesson 7

Create equations to represent known translations and reflections of a graph.
Identify a transformation needed to fit a function to data and represent the new function with an equation.

Scaling Outputs and Inputs

Lesson 8

Calculate the scale factor \(k\) needed to transform the output of a function to fit data.
Describe the effect of a scale factor on the output of a function.

Lesson 9

Calculate the scale factor \(k\) needed to transform the input of a function to fit a situation.
Describe (orally and in writing) the effect of a scale factor on the input of a function.

Putting It All Together

Lesson 10

Create new functions by adding, subtracting, multiplying, and dividing simpler functions with and without context.

Lesson 11

Compare and contrast different models for the same data.
Use transformations to create a function that models data given a simple starting function.

Alg2.5: Transformations of Functions