cobweb diagrams

Question 1

cobweb diagram

Answer 1

visual representation of DDS

Question 2

stable

Answer 2

if diagram moves towards fixed point

Question 3

unstable

Answer 3

if diagram moves away from fixed point

Question 4

unstable spiral

Answer 4

moving away from f.p
y=ax+b where a<-1

Question 5

stable staircase

Answer 5

moving towards f.p
y=ax+b where 0<=a<1
pos but less than 1

Question 6

unstable staircase

Answer 6

moving away from f.p
y=ax+b where a>1
pos

Question 7

square/periodic

Answer 7

y=-x/ y=-x+h
where line intersects with y=x line perpendicularly causing a square

Question 8

every point f.p

Answer 8

y=b
every point on line will be a fixed point as the line goes back and forth

Question 9

endless staircase

Answer 9

endless staircase with no fixed point.
where y=1x+b, line is parallel to y=x line
parallel lines never meet hence no f.p

Question 10

stable spiral

Answer 10

moving towards f.p
y=ax+b
where -1<a<=0

Question 11

cobweb graph

Answer 11

graph = map

xn+1 = 2xn + 3
graph: y=2x+3

Question 12

x and y values

Answer 12

values on x-axis are input to go into xn
values on y axis: output/ result xn+1

Question 13

fixed point

Answer 13

f.p is POI of 2 graphs

Question 14

how to draw

Answer 14

• Draw a set of axes
  
  • Draw y=x
  • Draw y=ax+b
  • NOTE - The f.p is @ POI of these lines
  • Starting at x0, draw a vertical line that hits y=ax+b
    Draw a horizontal line to y=x ( taking y output and turning it into input)
    repeat
    arrows!