This activity is designed for those students who are confused by the notation for inverse and the exponent negative 1. The two concepts are examined numerically, analytically and graphically with examples and questions. This activity would be appropriate as a tutorial for struggling students and would be a quick reinforcement for those who are solid in understanding the concepts of reciprocal functions and inverse functions.
Before the Activity
Students should be able to find the equation of the inverse of a function. They should be familiar with vertical and horizontal line tests, one-to-one, domain, symmetry, and know the reciprocal trig functions. It is also expected that students are familiar with graphs of basic polynomials and trig functions.
During the Activity
Students will complete the activity individually or working with a partner. The directions and questions within the activity will lead the student to understand the notation for inverse and the notation for -1 power are quite different concepts.
No worksheet is needed as the student will complete the activity by either orally responding to the questions with their partner or by recording the answers on paper, as the teacher directs.
After the Activity
The student should be able to distinguish between inverses and reciprocals by giving examples of graphs and using the correct notation for both. The only follow-up is for the student to submit his response to the final question of the activity.