Students have learning a lot about functions. In this unit, students saw how they can perform the four basic operations on functions. Students then looked at the resulting function and were able to determine what the domain of that new function was by looking at the domains of the original functions. After performing the four basic operations on functions, students learned that there is an additional operation that can be performed on functions, called the composition. Student learned how to evaluate the composition of two functions for a certain value of x. Next, students started to learn about inverse functions. They started by graphing a linear function and graphing its inverse by interchanging the x and y in the original function. Looking at this graph, we folded the paper so that the two lines overlapped. Students looked at the crease they had folded, and saw that it was the line y = x. Finally, we discussed how to verify that two functions are inverses by finding the compositions of the two functions.
Students graphed inverse functions and saw that they are reflected over the line y = x.