Students learn math concepts best when discovering mathematical patterns on their own rather than being told by the teacher. This activity is designed to have the students discover the rules for the shifting the graphs of functions horizontally by discovering them on their own. Students will be using an online visual tool, Desmos, in order to aid them in their discovery. Students can just as well use a graphing calculator if they own one.
1. Students have learned the basics of functions
2. Students have learned functional notation
3. Students have been introduced to the parent functions and their graphs
4. Students know how to graph a function by hand given a table of values
5. Students understand the domain and range of a function.
Students are first given a simple function and a table of values. They are then given a simple transformation of this function and are asked to create a new table of values showing where these points have been shifted. They are then to graph the points from the new table.
After this brief introduction, students are given a parent function with a dynamic variable (A) that allows the function to be transformed (ex. y=|x-a|). Students are then asked to use the online graphing application, Desmos, to graph the parent function while giving different values to the dynamic variable (A). Desmos allows students to transform a function using the slider feature. The slider feature enables students to change the value of the dynamic variable (A) which in turns transforms the graph. This helps students to discover patterns in a much shorter space of time then it would take if the students graphed each graph by hand.
What the Student will Discover
Students’s will learn how to manipulate the equation of a function so that its graph is shifted horizontally.
The activity consists multiple sections where each section explores a different transformation. It is expected that students will take several day to finish this activity. Students are asked to use Desmos to graph a function that has been transformed. The students are then asked follow-up questions to help them discover the pattern for transforming the function using that particular transformation.