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 reflecting of graphs across the axes 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=Ax). Students are then asked to use the online graphing application, Desmos, to graph the parent function while changing the value of a from positive to negative. The graph of the function will dynamically change as the sign of A is changed. 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 graphs is reflected across one of the axes.
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.