Transformations of Functions (ARC)
Ashley Berger, University of Oklahoma
Dustin Gaskins, University of Oklahoma
In the Functions and Modeling class, there is a high emphasis on establishing the relationship between the algebraic and the graphical representations of functions. One such way to establish this relationship that also challenges students to think about how two quantities can change simultaneously is through the study of function transformations. The goal of these activities is to take some already scaffolded exercises that explore the concepts of function transformations and provide a more hands-on, experimentation-oriented component that will allow students to more easily generalize the effects of a set of function transformations on a graph. In doing so, students should have concrete, visual examples to help solidify their understanding of the algebraic and graphical relationship between functions. Additionally, this activity should strengthen their covariational reasoning skills as they move from observing two quantities moving simultaneously to predicting how the two quantities will move simultaneously.
|
Vertical Transformations
|
This activity allows students to experiment within Desmos to explore the relationships between algebraic changes and the resulting graphical transformations. Activity 1 focuses on basic transformations where students explore one vertical transformation type at a time. Additionally, students should be able to relate the algebraic expression of the function transformation and the change in the original function’s domain and range.
|
|
Horizontal Transformations |
This activity allows students to experiment within Desmos to explore the relationships between algebraic changes and the resulting graphical transformations. Activity 2 focuses on basic transformations where students explore one horizontal transformation type at a time. Additionally, students are prompted to explore why horizontal transformations move in one direction when the notation might suggest the opposite direction.
|
|
Transformation Orders |
This activity allows students to experiment within Desmos to explore the relationships between algebraic changes and the resulting graphical transformations. Activity 3 focuses on transformations where students explore two transformation types at a time. First, the order of vertical transformations is considered, then the order of horizontal transformations.
|
This work is licensed under CC BY-NC-SA 4.0
