Lesson #23 Graphing the Greatest Integer Function

Recall that a GIF is a function where the output (y-value) jumps to distinct levels.

The easiest way to graph a GIF is by using a table of values.

X y

Graph f(x)=[x]

X y

-2 -2

-1 1

0 0

1 1

2 2

Counter Step Height

Step Length

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

bunits

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

Eg 2. Evaluate

f(4) = [4.4]

= 4f(-6) = [-6]

= -6

f(-5.4) = [-5.4] = -6

f(-7.1) = [-7.1] = -8

-1 0 1 2-2-3 3

Imagine a number line. The GIF always shift the value left, to the nearest integer.

Homework

Handout