Graph Plotter: Intsructions - PART I

 Online Graphing Calculator / free Scientific Calculator for mathematical functions and calculus. Thanks to this Graphing Calculator, you will be able to draw your mathematical functions online for free. Up to three functions can be plotted on the same graph. Therefore, three input fields are available to enter three formulas : f(x), g(x) et h(x). To use this online graphing calculator, you must make sure JavaScript is activated in your browser. Draw plots the image of the graph, Reset sets back the values that define the graph and Standard sets back display settings such as color,... All the mathematical functions defined hereunder can be used with the Scientific Calculator (free scientific calculator online) and with the Graph-Plotter (graphing calculator) as well. European Civil Aviation School Become a pilot !

Syntax: the following symboles can be used to build your function :

x Function variables
0-9 Numbers, ex. 178.62 You can use numbers of 300 digits as maximum. The output value (the result), for a non-log scale, will not be inferior to -100000 nor superior to 100000.
Very large numbers can be written in scientific language such as 3.7E54 for 3.7*1054. Very small numbers can be written like this 5E-23 for 5*10-23. Decimal numbers will be exact until the 12th digits.
. , Decimal separator may be the point or coma (as you wish), ex. 1.6 or 1,6
( ) [ ] { } < > Those three types of brackets are accepted, ex. {[(3+x)/(5-x)+7]*2}/(5*x^3). Each bracket opened must be closed. The type of bracket used does not matter.

# Used as separator in formulas that require more than one input value, ex. scir(x#5) to plot a half circle with a radius of 5
asy Plot a vertical asymptote for a given x-value, ex. asy(3) ou asy(e) pour x = 3 ou x = e
Q Contains a formula which may be a function of x itself. Q is defined by you at the bottom of the form on the right side (see Def. Q = ...). When you have defined Q, you can use this letter in your equation to plot the graph of f(x), g(x) or h(x). Q may be used as well in the calculator (see Calculate single values).

- Basic arithmetic operations

+ Plus, ex. x+1
- Minus, ex. 1-x
* Times, do not forget it, ex. you must write 3*x instead of 3x.
/ : Divided by, ex. 5/x or 5:x

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Constants

e Euler's number (base of natural logarithm ln); 2.718281828459
pi π 3.1415926535898
sq2 Square root of 2; 1.4142135623731
go Golden ratio; 1.6180339887499
d Feigenbaum constant, delta; 4.6692016091030

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- Basic functions

^ Power, ex. x^2 for x2. Roots can be written as follow: x^(1/3) or x^0.3333 for the cube root of x. Other example: e^(x+1) for e(x+1).

Roots of negative values (if the argument of the root is inferior to zero) may be plotted but only if the numerator of the power is 1 and the denominatorr of the power is odd (ex. x^(1/5)).
Thus, to calculate and/or plot the full graph (for value of x < 0) of f(x) = x^(2/3), you must write the function like this: (x^(1/3))^2

sqr Square root, ex. sqr(x) is the same as x^(1/2).
exp Exponent ex, ex. exp(x) is the same as e^x.
log Naperian logarithm (or natural logarithm) ln, ex. log(x)
log10 Decadic logarithm (base 10), ex. log10(x)
logn Logarithm to the base n, ex. logn(2#x) logarithm of x to the base 2, log2(x).

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- Trigonometric and hyperbolic functions

 sin Sine, sinus, ex. sin(x) cos Cosine, cosinus, ex. cos(x) tan Tangent, ex. tan(x) cot Cotangent, ex. cot(x) sin2 Sine square, ex. sin2(x) cos2 Cosine square, ex. cos2(x) tan2 Tangent square, ex. tan2(x) cot2 Cotangent square, ex. cot2(x) asin Arcsine, ex. asin(x) acos Arccosine, ex. acos(x) atan Arctangent, ex. atan(x) acot Arccotangent, ex. acot(x) sinh Hyperbolic Sine, ex. sinh(x) cosh Hyperbolic Cosine, ex. cosh(x) tanh Hyperbolic Tangent, ex. tanh(x) coth Hyperbolic Cotangent, ex. coth(x) asinh Area Hyperbolic Sine, ex. asinh(x) acosh Area Hyperbolic Cosine, ex. acosh(x) atanh Area Hyperbolic Tangent, ex. atanh(x) acoth Area Hyperbolic Cotangent, ex. acoth(x) sca Secant, ex. sca(x) csc Cosecant, ex. csc(x) asca Arcsecant, ex. asca(x) acsc Arccosecant, ex. acsc(x) scah Hyperbolic Secant, ex. scah(x) csch Hyperbolic Cosecant, ex. csch(x) arscah Area Hyperbolic Secant, ex. arscah(x) arcsch Area Hyperbolic Cosecant, ex. arcsch(x)

deg Converts a radian number to a degree number, ex. deg(pi) gives as an output value (the result) 180°
rad Converts a degree number to a radian number, ex. rad(180) gives as an output value 3.14159 rad
(Just check it with the Online Graphing Calculator / free scientific calculator online )

If you want to plot a trigonometric function, for instance cos(x), be aware that the values showed on the x-axis are radian numbers. If you want it in degrees, you must type in the f(x)-input field the following formula : cos(rad(x))

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- Non-differentiable functions

abs Absolute values, ex. abs(x)
fac Factorial (!), ex. fac(4) which is 4! = 4.3.2.1 = 24, fac(x) is the same as x! . Non-integer numbers are rounded.

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Graph Plotter's control panel description

Just try everything you want, ... you won't break anything!

You can pick Transp. (transparent) everytime you are asked to choose a color. If you select Transp. you must switch the antialiasing off. Transparent image can be displayed only with png et gif images (it does not work with jpeg format).

Functions:

On the right side of your function, you can define the color of the curve plotted. You can also decide if the equation will be shown or not on the image with Show term. You can also choose between a curve made of connected dots (connect) or separated dots (dots).
Derivative computes and plots the derivative of your function. You will see written on the graph : f'(x)=[...]'.
With from ... to, you can define the domain on which you want your function to be plotted. Type in values of x. If you leave it empty, your function will be graphed on his entire domain. Constants such as pi (for instance) are allowed.

Display properties:

With Image type you will be able to choose between png (compression level 1), gif (GIF87a) or jpeg (quality level 90 %).
Range x-axis (or y-axis) from... to... defines the window in which you wish to plot your function. The maximum entry value is 100000 (or -100000). With a logarithmic scale, the output value can reach 10300. Constants such as pi (for instance) are allowed.
Tick marks on x-axis (or y-axis) defines the number of tick marks you want on the x-axis (or y-axis). You will see real numbers above those tick marks, which are graduations. The maximum allowed is 100 graduations.
Vertical lines / Horiz. lines defines the "density" of the grid. You can specify the number of vertical and horizontal lines that will form the grid. The maximum is 100 lines.
Decimal places defines the number of displayed decimal places in the caption. Maximum is 12.

Log. scale x : (or y) determines if the x-axis (or y-axis) will be displayed linear or logarithmic. "No" means linear. You can choose between different logarithmic bases such as 2, e, 10 ou 100, or even type in a value that you have chosen. The logarithmic display does not allow to show integrated or derivated graphs nor iterations!

The checkboxes, if checked, will show on the graph the grid, x- and y-axis, graduations (tick marks and its caption), frame of the image, and error messages if an error has been made.

With Def. Q= you can define a formula (that contains the variable x if you whish) or a constant. Then you will be able to use Q in the three input fields f(x), g(x), ou h(x). You can also use Q with the Calculator (see Calculate single values).

Antialiasing is used to improve image quality.

The displayed graph will never be an exact image of the function. It will rather be an approximation as close as possible to the reality.

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Calculate single values : Scientific Calculator

Type in a function (incluing the variable x if you want to) with the same syntax as described hereabove or click on 1, 2 ou 3 to insert respectively the function f(x), g(x) or h(x). Next, type in a value for x in "Input value(s) x:" and click on Calculate. The result is rounded according to the number of decimal you have entered in Decimal places . Unfortunately, the value of the functions phi, derivative, integral and iterations cannot be computed in this field.
You can introduce more than one input value: "Input value(s) (x): ". To do so, introduce the x values separating it with spaces (ex. 3 5 7 1 0). The result will be displayed as a single row array.
This tool may be used as well as a simple scientific calculator : type in the field "Function:" the arithmetic terms such as (2*2.5)/5 without any x value, next click on "Calculate" to get the result, whish is 1 in this example.

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The Instructions PART II will help you to use this online graphing calculator / scientific calculator and graph plotter more efficiently. You will learn more about: Non-differentiable functions, Probability functions and statistics, Special functions, Programmable functions, Iterations & fractals, Differential and integral equations.