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.

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

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

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

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

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

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

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