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.
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The graph of the function f is
{ (x,f(x)) | x ∈ {0,1,2,3,4,5,6} } =
{(0,0),
(1,0),
(2,6),
(3,0),
(4,0),
(5,0),
(6,0)}
The function f evaluated at the elements of its domain {0,1,2,3,4,5,6} is:
f(0)=0,
f(1)=0,
f(2)=6,
f(3)=0,
f(4)=0,
f(5)=0, and
f(6)=0.
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, 3, 4, 5, 6}
The function f is not invertible because f(0)=f(1).
The function f is not the identity function on {0,1,2,3,4,5,6}.