1. Activity 4.2 Greatest Integer Graphs
COMMON CORE STATE STANDARDS
HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
HSF-IF.C.7b Graph piecewise-defined functions, including step functions and absolute value functions.

2. FORMULA: Greatest Integer “Step Functions”
(h,k) = starting point (if b=1)
h = horizontal shift (bx-h)=0
k = vertical shift
a = distance between each step
b= length of each step

3. EXAMPLES: (h,k) starting point: _____ a= dist. btw _________
b= length step ________
(0,0)
Domain: All Real
Range: All Integers

4. (h,k) starting point: _____
(- 4,0)
(h,k) starting point: _____
a= dist. btw _________
b= length step ________
Domain: All Real
Range: All Integers

5. (h,k) starting point: _____
(0,3)
(h,k) starting point: _____
a= dist. btw _________
b= length step ________
Domain: All Real
Range: All odd Integers

6. (h,k) starting point: _____
(0,3)
(h,k) starting point: _____
a= dist. btw _________
b= length step ________
Domain: All Real
Range: All Integers

7. (h,k) starting point: _____
(3,1)
(h,k) starting point: _____
a= dist. btw _________
b= length step ________
Domain: All Real
Range: All Integers

8. (h,k) starting point: _____
(- 4 ,- 2)
(h,k) starting point: _____
a= dist. btw _________
b= length step ________
Domain: All Real
Range: All Integers