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

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

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)

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

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)

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)

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)

Let’s try another example. f -1 f

Let’s try another example. f -1 f

One last example. . . f -1 f

One last example. . .

One last example. . .

One last example. . .