1. “Cobweb” diagrams

2. Affine Difference Equations---Slope bigger than 1

4. Affine Difference Equations---Slope less than -1

5. What if we start iterating with a point that lies to the left of the fixed point? Affine Difference Equations---Slope smaller than 1

6. Affine Difference Equations---Slope in (-1,0).

7. Affine Difference Equations---Slope equal to1

8. Conclusions: Long term behavior of solutions to affine difference equations: If, the sequence (A(n)), n = 1, 2, 3,... “blows up”. That is, The fixed point is a repelling fixed point. If, the sequence (A(n)), n = 1, 2, 3,... Converges to the fixed point of the function. That is, The fixed point is an attracting fixed point.