Program for drawing graphs of functions

Type the formula:
\(f(x) = \)
Type in the given field founction formula, for example:
x^2-5
and then click "Draw".
If you want to simultaneously draw graphs several functions , then separate them with a semicolon patterns, for example:
x^2-5;2x+1
The program interprets the patterns of functions in accordance with the order of execution of operations (eg, exponentiation takes precedence over multiplication, and multiplication takes precedence over addition).
Remember that you can use parentheses to enforce the correct sequence of actions.
The program supports six parameters a, b​​, c, m, p and q. After generating function, the parameters can be modified using the slider. Example of function with parameters:
ax^2-x + c
Formulae
Additional settings
Canvas size: (560/1600)
Sets the physical size of the coordinate system.
If the coordinate system does not fit on the right side, it will be moved on the bottom.

Accuracy: (100/200)
Higher accuracy value set in two cases:
1) In a situation where the function very quickly changes its value (eg, the function has a vertical asymptote).
2) In a situation where we want to calculate the extra zeros. At the low accuracy of zero can be calculated with small error, or can not be described at all.
Note: If the accuracy is high, than the graph is generated slowly. If you don't generate very complex functions, you shouldn't set high accuracy value.
Grid Axis Ox Axis Oy Special points
Describe axes
Adds the coordinates on the axes Ox and Oy.
Note: Disable automatic selection of zero, the intercept Oy and asymptotes.

Zero of function
Selects and calculates the zeros of functions.
Note: If you haven't calculated all of place zero than should increase the accuracy by the slider above.
Note: Disable automatically selects the coordinate axes Ox and Oy.

Point of intersection with Oy
Selects and calculates the intersection graph of axis Oy .
Note: Disable automatically selects the coordinate axes Ox and Oy.

Extremes
Calculates and selects the extremes of function.
Note: If the extremes of function are not calculated accurately, you should increase the accuracy by the slider above.

Asymptotes
Calculates and selects the vertical and horizontal asymptotes of the function (if any).
Note: Disable automatically selects the coordinate axes Ox and Oy .
Note: If the asymptote function are not calculated accurately, it should increase the accuracy by the slider above.

Derivatives
Draw a graph of the derivative function additionally.
Note: If you are working with only one function, than its derivative is drawn in orange.
If you work simultaneously with several functions, than their derivatives will be drawn color slightly lighter than the original.


Integral
Counts the integral of the selected area
 for x ∈ (; )
In these fields, you can specify the interval at which you want to calculate the integral.
If you don't enter any value, than the integral is calculated over the visible range of arguments.
Note: The maximum range of the arguments on which the integral is calculated is the range shown on the chart. If you want to calculate the integral to a larger area, it just zoom out the graph.
Zoom: 40
Use right mouse button to zoom the canvas

Center of canvas: (0; 0)
Use left mouse button to move the canvas

Select the points with coordinates x =
When you want to select multiple points, then enter the coordinates x-those separated by semicolons.

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Available operators
Operator Function Example Example with parameter
+ addition 2x+3 ax+b
- subtraction 2x-3 ax-b
* multiplication 2*x a*x
/ division 3/x a/x
^ exponentiation x^3 a(x-b)^4+c
sqrt() roots sqrt(2x) sqrt(ax)-b
| • | absolute value |x+5|-4 |x-p|-q
log() he natural logarithm log(x) log(ax)-b
sin() sine sin(x^2) a*sin(bx)+c
cos() cosine cos(3x-1) a*cos(bx-p)+q
tg() tangent tg(x) tg(x/a)
ctg() cotangent 3ctg(x/10) a*ctg(x/b)
The program supports six parameters: a, b, c, p, q, m, which may be given in the formula function instead of numerical coefficients.
After generating a graph parameter values ​​can be changed dynamically by the sliders.
Patterns of typical functions with parameters
Name of function Function formula
The linear function ax+b
The quadratic function (general form) ax^2+bx+c
The quadratic function (multiplicative form) a(x-b)(x-c)
The quadratic function (canonical form) a(x-p)^2+q
The function of the absolute value a|x-p|+q
A homographic function a/(x-p)+q
3 degree polynomial function ax^3+bx^2+cx+p
The program can display graphs of several functions at the same time.
If you want to simultaneously draw graphs of several functions, then separate them with a semicolon.
If you draw graphs of several functions at the same time, than in the "Additional settings" there will be new options such as: computing and selecting points of intersection, or the count field (integrals) between the indicated functions.
Examples of the analysis of several functions
Description of the example Formula
The linear and quadratic function ax+b;c(x-p)^2+q
Analysis of the number of solutions of the equation with a parameter:
x2 - x - 6 = m		 x^2-x-6;m
Area bounded by the paiabola and the axis Ox ax^2+bx+c;0
The area under the sine a*sin(bx);0
Graphical solution of inequalities:
xsin(x) > mx^2
depending on the parameter m		 xsin(x);mx^2
Number of solutions of equation:
|||x - a| - b| - c| = m
depending on the parameter a, b, c oraz m		 |||x-a|-b|-c|;m
Calculation of the field described by the system of inequalities: \[\begin{cases} \frac{1}{x}\gt m\cdot \sin x \\ \frac{1}{5}\lt x\lt 5 \end{cases} \] w zależności od parametru \(m\) 1/x;m*sin(x)
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