14-­‐12-­‐12 World 3-2
Graphing and Transformations of the
Greatest Integer Function
Recall, a GIF is a function that rounds down any input
value in the [ ] to nearest integer.
GIFs can be graphed and look like steps on a staircase.
The width of the steps, height difference between steps
and shifts are affected by function transformations.
Graph f(x)=[x]
The function f(x) = [x] can be transformed.
g(x) = a[b(x-h)]+k
a : is the counter step height (“vertical stretch”)
b : the step length of 1 units
b
h : horizontal shift by h units to the right
k : vertical shift up k units
€
a<0 b<0
a>0 b<0 a<0 b>0
a>0 b>0
Vertex
Counter Step Height
World 3-2
Graphing and Transformations of the
Greatest Integer Function
Step Length
a) Determine the equation
y = [x]
Greatest Integer Func2on: Graph Challenge 1 14-­‐12-­‐12 b) Determine the equation
y = [x] + 2
c) Determine the equation
y = [x-3]
d) Determine the equation
y = 2[x]
e) Determine the equation
y = 2[x+1] + 2
f) Determine the equation
y = -3[x-1] + 2
g) Determine the equation
y = -2[-x] + 3
2 14-­‐12-­‐12 h) Determine the equation
i) Determine the equation
j) Determine the equation
k) Determine the equation
l) Determine the equation
Homework
Handout
3