Inverses

Graph {(1,2), (2,-4), (5,2), (2, 0), (-1, 4)} ?

{(2, 1), (-4, 2), (2, 5), (0,2), (4, -1)}

These graphs are called inverses of each other.

Graph the points as (y, x)

Example 1:A)Graph the inverse of the function shown in a different color

B) Graph the line y = x in a different color.

C) In the inverse a function? Explain

x y -1

Inverse

x y

Function

It may help to make tables of values.

Yes, it passes the vertical line test.

D) What is the relationship of the 2 graphs with respect to y = x ?

The are reflections of each other across the line.

A)Graph 2 6y x

D) Write an equation for the inverse.

B) Graph its inverse in a different color.

C) Is the inverse a function? Explain.

Example 2:

Yes, it passes the vertical line test.

1 13

2y x

A)Graph

B) Graph its inverse in a different color.

C) Is the inverse a function? Explain.

Example 3:

No, it does not pass the vertical line test.

2( ) ( 2)f x x

A)Graph

B) Graph its inverse in a different color.

C) Is the inverse a function? Explain.

Example 4:1

( ) 2 42

g x x

D) Write an equation for the inverse.