Being able to recognize how changes in the equations of a function could affect the shape of the function’s graph is a important component of BC’s Pre-Calculus 12 curriculum. The concept applies to all the different types of functions encountered in the course, and plays a role in helping students understand the shapes of different graphs.
This concept is challenging for students because it is easy to build misconceptions about the effect of changing certain variables in the equation. For example, adding a value of +k to a function f(x), would give an equation in the form of y=f(x)+k, and would translate the original graph k units up on the grid. On the other hand, replacing x with x+k, would give an equation of the form y=f(x+k), and would move the graph to the left, which is counter-intuitive because left is usually associated with negative numbers. This chapter has other similar concepts that could make it hard for students.
I have created a visual for a TGEM activity that could help students master the concepts in function transformation: https://magic.piktochart.com/output/23407439-etec-533-tgem-desmos
1. Generate: The teacher will preview two different graphs of parabolas and ask students to note the differences between the shapes of the graphs, or where they are located on the coordinate plane. Afterwards, students will be given the equations that correspond to each graph and be asked to make predictions on how different numbers in the equation could affect the shape and position of the graph.
2. Evaluate: The teacher will provide the Desmos activity “What is My Transformation”. The activity serves as an evaluative exercise for students and will allow them to determine whether the predictions they have set in the beginning of the lesson were correct.
3. Modify: After working through the activity, the teacher will regather the class, and ask for students to provide some of the facts that they were able to establish about modifying the equation of a graph. The teacher will also ask students to name some of the misconceptions that they came up with, and be asked to explain what led them to these incorrect assumptions. The point of emphasis is to crowdsource a list of possible areas where students could make mistakes.