More on Linear Iteration Rules

I've doing a lot of work with linear iteration rules.

I figured the following out:
Given Ax + B, if A = 1
then
B > 0 orbits go to infinity
B = 0 all points are fixed
B < 0 orbits go to negative infinity

But,
What would happen if A =.999? Would orbits be attracted to a fixed point?
If so, what would the fixed point be?

Thanks,
Alex.


.

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