SWBAT graph and analyze a greatest integer function
Warm up
Write the function for each graph.
a)
b)
SWBAT graph and analyze a greatest integer function
(Lesson 6 - 2- 2)
Functions whose graphs resemble sets of stairsteps are known as step
functions. The most famous step function is the greatest integer
function, which is denoted by [[x]] and is defined as
f(x) = [[x]] = the greatest integer less than or equal to x.
f(x) = int(x)
The basic characteristics are summarized.
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Domain (- ∞, ∞)
Range: the set of integers
x-intercepts: in the interval [0, 1) and y-intercept: (0, 0)
Constant between each pair of consecutive integers
Jumps vertically one unit at each integer value
SWBAT graph and analyze a greatest integer function
(Lesson 7 - 2- 2)
The greatest integer function, or rule which produces the "greatest integer
less than or equal to the number" operated upon, symbol [x] or sometimes
[[x]].
If the number is an integer, use that integer.
If the number is not an integer, use the next smaller integer.
Example 1) f(x) = [x] Evaluate the function when
x =- 1, 2,
3 1
,
2 4
Example 2) f(x) = [x] + 1 Evaluate the function when
x =- 1, 2,
3 1
,
2 4
Step Functions:
(1)
f ( x)  x
(2)
f ( x)  2x
(3)
f ( x)  2 x
(4)
f ( x)   2 x
Example 2) Graph
y = ([x]) 2 on the interval -2 ≤ x ≤ 3