1. a. Write a function, f(x), to represent the 5 bonus points.
Warm Up: A math test has a bonus question.  The directions simply state that if you answer the question correctly you will receive 5 bonus points and then your test grade will be increased by 7%.
(Let x = test score before answering the bonus question.)
a.  Write a function, f(x), to represent the 5 bonus  points.
b.  Write a function, g(x), to represent just the percent of increase.
c.  Explain the meaning of g(f(x)).
d.  Find g(f(75))

2. Lesson 1.5-1 Inverse Functions
Objective: Define inverse functions and algebraically verify that two functions are inverses.

3. NOTE: The inverse of a function may not always be a function!
Notation:
NOTE: The inverse of a function may not always be a function!

4. Ex. 1: Calculate the inverse of the following functions

5. Ex. 2: Calculate the inverse of the following functions1 -2 -1 3 4
f(x) 2 x
f-1(x)

6. Two Functions are inverses if:
The domain of f is equal to the range of f -1, and the range of f is equal to the domain of f -1.

7. To verify that two functions are inverses:

8. Ex. 3: Determine if the functions are inverses

9. Ex. 4: Determine if the functions are inverses

10. Ex. 5: Determine if the functions are inverses

11. Graphs of Inverse Functions

12. Graph the inverse points…

13. Ex. 6: Determine if the inverse is a function

14. Horizontal Line Test: Determines if the function is invertible

15. Ex. 7: Use a graphing calculator to see if an inverse function exists

16. Ex. 8: Find the inverse algebraically

17. Ex. 9: Find the inverse algebraically

18. Ex. 10: Find the inverse algebraically

19. Ex. 11: Find and verify the inverse of the given function

20. Closing Thoughts: Synthesis Calculate, verify, and graph the inverse.