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Let's graph the inverse functions we had in the last lesson on the same graph and see what happens:
 

f( x ) = x + 3andg( x ) = x - 3

a graph of f( x ) and g ( x )

There are two big things I want you to notice:

1 )  a graph of f( x ) and g( x ) ... they are mirror images across the line y = x

They are mirror images over
the line
y = x.

(In other words, they are symmetric with respect to the line y = x.)

 

2 )  a graph of f( x ) and g( x ) ... each point on the f( x ) graph has a reversed partner on g( x ) ... ( -3 , 0 ) has the partner ( 0 , -3 ) ... ( -2 , 1 ) has the partner ( 1 , -2 ) ... ( -1 , 2 ) has the partner ( 2 , -1 ) ... ( 0 , 3 ) has the partner ( 3 , 0 )Notice that every point on f(x) has a reversed partner on g(x).

(0, 3) has (3, 0) as a partner and so on.

So, just remember this:

Every (x, y) has a (y, x) partner.