# dynamic colors

## Introduction

Following applet illustrates two ways to use dynamic colors.
• The colors of the sign of a function f and the color of a Point P depent on a given condition.
• The colors of a slider s and a point C are calculated out of a variable value.
• sign of a function: The sign of a function `f(x)= ax + b` depends from the values of a and b.
• color of a point P: Point P colors green when it's on the graph of f and red if it's not.
• color of a slider: The color of slider s changes while moving the slider.
• color of a point C: The color of point P changes if you drag it along the segment l.

## How do you do this?

• Sign of the function f: Create: - a slider a from -4 to 4 with increment 0.5 - a slider b from-4 to 4 with increment 0.5 - a function `f(x) = a x + b` - a number zero = -b/a - a number `c = Integral(f, -50, zero)` - a number ```d = Integral(f, zero, 50) ```Open the Properties of c and d, select the tab Advanced and define their dynamic colors so that a negative value will color red and a positive value will color green.  ﻿ colors of c﻿ colors of d﻿ ﻿Red: `If(c < 0, 1, 0)` `﻿If(c > 0, 0.7, 0)` ﻿Green: ﻿`If(d < 0, 1, 0)` `﻿If(d > 0, 0.7, 0)` ﻿Blue: ﻿`0` `﻿0`
• Color of the point P: Create a point P, open its Properties and select the tab Advanced. Define its colors so that P colors green when it's on the graph and green when it's not.  ﻿Red: `If(Distance(P, f) > 0, 1, 0)﻿` ﻿Green: `﻿If(Distance(P, f) ≟ 0, 0.7, 0)` ﻿Blue: ﻿`0`
﻿
• Color of the slider s: Create a slider from `0` to 1 with increment 0.1. Define its color in the tab advanced of its Properties:  ﻿Red: `﻿s` ﻿Green `﻿0` ﻿Blue `﻿1-s`
Moving the slider from 0 to 1 its color will change from blue to red.
• Color of the point C: Create: - the Segment l between the points A and B: `l = Segment(A,B)`. - the Point C on the segment. - the Segment g between the points A and C: `g = Segment(A,C)`. Define its colors so that C will color from black to green while dragging it on the segment.  ﻿Red: `﻿0` ﻿Green: ﻿`g/l` ﻿Blue: ﻿`0`