1. {(1, 1), (2, 4), (3, 9), (4, 16)}
one-to-one
{(-2, 4), (-1, 1), (0, 0), (1, 1)}
not one-to-one

2. Theorem Horizontal Line Test
If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one.

3. Use the graph to determine whether the function
is one-to-one.

4. Use the graph to determine whether the function
is one-to-one.

5. ( ) ( ) y f x = ( ) Let f denote a one-to-one function . f The1
The
inverse of f
, denoted by
, is a ( ) f x - = 1
function such that
for every x ( ) f x - = 1
in the domain of f
and
for f - 1
every x
in the domain of .

6. Domain of f
Range of f

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

8. f x ( ) , = - 5 3 f x ( ) , = - 5 3
Find the inverse of
Find the inverse of 3 3
The function is one-to-one.
The function is one-to-one.