1. One-to One Functions Inverse Functions
Section 1.9

2. Ways to Represent a Function
Map
Set of ordered pairs
Graph
Equation

3. A function is one-to-one if any two different inputs in the domain correspond to two different outputs in the range. A function is not one-to-one if two different inputs correspond to the same output.

4. Page 100
9. 13.

5. Horizontal-line Test If every horizontal line intersects the graph of a function f in at most one point, then f is one-to-one.

6. Page 101

7. A function that is increasing on an interval I is a one-to-one function. A function that is decreasing on an interval I is a one-to-one function.

8. f-1 Inverse Function of f
Receives as input f(x)
Manipulates it
Outputs x
The domain of f = The range of f-1
The range of f = The domain of f-1

9. Page 101

10. f-1 (f(x)) = x where x is in the domain of f f-(f-1(x)) = x where x is in the domain of f-1

11. Page 102
37.

12. Pages (10-46 even)

13. Inverse Functions
Section 1.9

14. The graph of a function f and the graph of its inverse f-1 are symmetric with respect to the line y = x

18. Page 102
49.

19. If a function is one-to-one, we can find its range by finding the domain of the inverse of the function.

20. Page 102
63.

21. If a function is not one-to-one, then its inverse is not a function
If a function is not one-to-one, then its inverse is not a function. An appropriate restriction will sometimes yield a new function that is one-to-one. Example: page 99

22. Pages (48-80 even)