Transformations of Functions (Lesson 1.5 Day 1)
Unit 1  Day 5
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Learning Objectives

Apply vertical and horizontal shifts and stretches to parent functions to graph the transformed functions

Given an equation, describe the transformations from the parent function

Use the knowledge of transformations to determine the domain and range of a function.
Quick Lesson Plan
Experience First
Today students work on another Desmos activity to connect analytical and graphical representations of transformations. After having studied six of the primary parent functions in the previous lesson, students are ready to explore how many other functions can be created from the parent functions.
To prepare for today’s lesson, create a class code for the “What’s My Transformation” activity on Desmos. Students will also need colored pencils to trace the transformed parangulas.
Allow students time to explore and test conjectures in this activity. Using Desmos as a tool allows students to make predictions and see the result. Students transition from dragging a “parangola” across the page to translating it using function notation. They observe patterns and are asked to make generalizations about what makes a function move up, down, left, or right. Various screens ask students to summarize their findings. Encourage students to write these summaries on their papers as well.
We have found that having two students share one computer really increases communication and fuels sense making. Slide 13 is challenging, and students benefit from hearing the ideas others have tried.
Formalize Later
No margin notes are offered in this activity because we believe the students’ findings are best consolidated in a table like the one offered in the Important Ideas section. This structure note taking allows students to connect symbolic and verbal representations.
Ask students why the notation f(x2) represents a shift to the right 2 units. Push students beyond an “it’s always the opposite” explanation. Although this concept can be confusing, a concrete example can help. If f(x)=x^2, then the original function has an output of 36 when x=6. However, for the transformed function f(x2), the output of 36 is reached only when plugging in x=8. Thus, the same output of 36 occurs two units later than it did on the original function, demonstrating that f(x2) represents a shift two units to the right. It’s easier to see this relationship when comparing a common output rather than comparing the yvalues at the same input. Question 4 on the Check Your Understanding has students reason through this idea with a contextual example.