Let the graph of the function

f : {0,1,2,3,4,5,6} → {0,1,2,3,4,5,6}

be given by the plot below.

Click on white pixels to change the graph of the function f.

f(x)
6
5
4
3
2
1
0
0 1 2 3 4 5 6 x

The graph of the function f is

{ (x,f(x)) | x ∈ {0,1,2,3,4,5,6} } = {(0,5), (1,6), (2,2), (3,0), (4,4), (5,4), (6,1)}

The function f evaluated at the elements of its domain {0,1,2,3,4,5,6} is:

f(0)=5, f(1)=6, f(2)=2, f(3)=0, f(4)=4, f(5)=4, and f(6)=1.

The image of the function f is

f({0,1,2,3,4,5,6}) = { f(x) | x ∈ {0,1,2,3,4,5,6} } = { 0, 1, 2, 4, 5, 6}

The function f is not the identity function on {0,1,2,3,4,5,6}.

The function f is not invertible because f(4)=f(5).