greatest integer function, af(bx-c)+d

Enter negatives as "-x" rather than "- x" Input a number

The greatest integer function, [x], rounds down to the lower integer or "floor."

There is no formal name for the round up function other than round up or "ceiling."

There is no formal name for the rounds to the nearest integer or multiple.

Some of the html code and Excel functions are listed here. The html math functions (used here) include these & others: Math.ceil() Round up. Math.floor( ) Round down. Math.round( ) Round to the nearest integer. Excel Formulas Include These & Others: =FLOOR.MATH(x,this multiple of y) Rounds x down to the nearest integer that is a multiple of y . =FLOOR.MATH(x) Rounds x down to the nearest integer, [[x]].

IN MATH: 1. n. the function, or rule which produces the "greatest integer less than or equal to the number" operated upon, symbol [x] or sometimes [[x]].

The greatest integer function is a piece-wise defined function.

: If the number is an integer, use that integer.; If the number is not an integer, use the next smaller integer.

https://www.hrblock.com/tax-center/filing/states/new-jersey-nj-tax-rate/
Income Tax Bracket	Tax Rate 2023-24
$0	to	$20,000	1.4%
$20,001	to	$35,000	1.75% minus $70.00
$35,001	to	$40,000	3.5% minus $682.50
$40,001	to	$75,000	5.525% minus $1,492.50
$75,001	to	$500,000	6.37% minus $2,126.25
$500,001	to	$1,000,000	8.97% minus $15,126.25
$1,000,001	and above	 	10.75% minus $32,926.25

	Real world uses for a step function or a greatest integer function or one of its "children" include:
* determining the dosage of a medication by weight of the patient
* computation of NJ sales tax. (now usually just computed as a percent without a tax table)
* computing postage or shipping costs.
* determining income tax bracket. For example:
Income Tax Bracket		Tax Rate 2023-24			slope (% as decimal)	tax function
$0 to $20,000				1.4%					1.4% is .014		.014
$20,001 to $35,000		1.75% minus $70.00		1.75% is .0175 	1.75x -70
$35,001	to $40,000		3.5% minus $682.50		3.5% is .035		.035x - 682.50
$40,001	to $75,000		5.525% minus $1,492.50	5.525% is .0525	.0525x -1492.50
$75,001	to $500,000		6.37% minus $2,126.25	6.37% is .063		.0637x - 2126.25
$500,001 to $1,000,000	8.97% minus $15,126.25	8.97% is .0897	.0897x - 15126.25
$1,000,001 and above	 	10.75% minus $32,926.25	10.75% is .1075	.1075x - 32926.25
from: https://www.hrblock.com/tax-center/filing/states/new-jersey-nj-tax-rate/

[[x]].gsp Sketchpad -- greatest integer function, also a[[bx+c]] + k
WARNING!! - Geometer's Sketch Pad does not have a greatest integer function. This graph is a fake and has issues.
1 - changes a & d
2 - changes c
3 - changes b
4 - changes b & c
5 - changes a, b, c, & d
6 - sine function w/A, B, C, D
7 - sine function w/A, B, C, g(x)
8 - hidden files that make the images happen
piecewise.gsp Sketchpad -- graphs a piecewise defined function when left function and right function and the x-value for the boundary are edited -- endpoints are not shown.
More Examples of Composite Functions
Absolute Value Function, |x|
What's a Function? - Index on topics like "How Functions Are Composed or Created", "Polynomial & Rational Functions"
$library$ - Function and Relation Library - Many functions w/their features & graphs

$[MC,i. Home]$ $[Table]$ $[Words]$ $Classes$

[Good Stuff -- free & valuable resources]

$[next]$ $[last]$