1. The graphs of f and f -1
How are they related?

2. Some Preliminary Thoughts
Suppose we have some points in the plane . . .

3. What happens if we switch their x and y coordinates?
(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(2,-2)
(-1,-1)
(2,-4)

4. (1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(2,-2)
(-1,-1)
(2,-4)

5. The line y = x serves as a “mirror”!
(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(2,-2)
The line y = x serves as a “mirror”!
(-1,-1)
(2,-4)

6. That is, each point is reflected across the line
(1,5)
(3,3)
(-4,2)
(-2,2)
(5,1)
(-1,-1)
(2,-2)
That is, each point is reflected across the line
y = x.
(2,-4)

7. f -1 f Suppose we have a one-to-one function f.
To get f -1 from f, we switch every x and y coordinate.
(4,6)
f -1
(2,3)
(6,4) f
(3,2)
(-1,-1)

8. Let’s try another example.
f -1
(1,5) f
(5,1)
(-0.5,-3)
(-0.5,-3)

9. Let’s try another example.
f -1 f

10. One last example. . .
f -1 f

11. One last example. . .

12. One last example. . .

13. One last example. . .