In this lesson, students combine horizontal and vertical translations at the same time. They continue analyzing a context from a previous lesson to address the common misconception that subtracting from the input will result in a translation to the left. Next, students apply this understanding to a new context, where they compare multiple ways to translate a curve to fit data. In the following lessons, students focus on transformations involving reflections of graphs across axes. Reflections, like vertical and horizontal translations, are examples of rigid transformations which means that they do not change the general shape of the graph.
Throughout the lesson, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). In particular, students begin the lesson by describing how to transform a graph to match other graphs. They return to these graphs in the Lesson Synthesis where they use function notation to describe one graph as a transformation of another.
- 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 $f(x+k)$.
- Let’s translate graphs vertically and horizontally to match situations.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can write equations to represent vertical and horizontal translations of graphs.
- I understand the relationship between graphs and equations describing horizontal translations.