1. Review Warm-up: Find the Domain of Each Function

2. Text search:3.7 pp.265 What is a one-to-one function? How can you tell if a function is one-to-one by examining the graph? Create 2 one-to-one functions and 2 functions that are not one-to-one functions.

3. Find a function that “ “undoes”each equation

4. OK, but is there an easier way than trial and error Yes, switch x and y and solve for y Try it for the examples you just figured out

5. Exploring inverse functions (on big paper) For your function A,B,C,D,E or F State the inverse function, label it as Create a table of values for the function and its inverse. Be mindful of what numbers to use as inputs to the inverse function Graph the function and its inverse on the same set of axes Compose the function and its inverse in both orders

6. Conclusions: An inverse function “undoes” the original function Its ordered pairs are reversed The graph of a function and its inverse are reflections over the line y=x The composition of the two functions yields x

7. Hmmm… How can we restrict the domain of so that it is a one-to-one function?

8. Inverse Functions in a Problem Context 3.7 #76, Toricelli’s Law A tank holds 100 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 40 minutes. Toricelli’s Law gives the volume of water remaining in the tank after x minutes as. Find, What does it represent? Find, What does your answer represent?

9. Homework Preview:

10. Find the inverse function for

11. Homework Preview Use Inverse Function Property to verify that f and g are inverses of eachother (composition)

12. Reminders... Project due Tuesday Classwork 3.7 #70,72,75,83 (we did 76) Homework 3.7 #21-40

13. Homework Quiz A. B.Find the inverse of g(x): C. Use composition to verify that f and g are inverses