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This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
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Various forms of function formulas
Name  Formula  Legend 
Exponential function in general form  Show source$y={ a}^{ x}$ 

Exponential function with base e (often written as exp(x))  Show source$exp(x)={ e}^{ x}$ 

Homographic function in general form  Show source$y=\frac{ a~ x+ b}{ c~ x+ d}$ 

Function b/x  Show source$y=\frac{ b}{ x}$ 

Linear function in slopeintercept form  Show source$y= a~ x+ b$ 

Linear function in pointslope form  Show source$y=\mathrm{a}\left( x x_0\right)+ y_0$ 

Linear function in constantslope form  Show source$\frac{y  y_0}{x  x_0} = \frac{y_1  y_0}{x_1  x_0}$ 

Zero of the linear function from constantslope form  Show source$x=\frac{ y_0\cdot\left( x_1 x_0\right)}{ y_1 y_0}+ x_0$ 

Quadratic function in standard form  Show source$y= a~{ x}^{2}+ b~ x+ c$ 

Quadratic function in factored form  Show source$y=\mathrm{a}\left( x x_1\right)~\left( x x_2\right)$ 

Quadratic function in vertex form  Show source$y={\mathrm{a}\left( x h\right)}^{2}+ k$ 

Function asymptotes
Name  Formula  Legend 
Vertical asymptote of homographic function  Show source$x=\frac{ d}{ c}$ 

Horizontal asymptote of homographic function  Show source$y=\frac{ a}{ c}$ 

Function discriminant
Name  Formula  Legend 
Discriminant of homographic function  Show source$D= a\cdot d b\cdot c$ 

Discriminant of the quadratic function  Show source$\Delta={ b}^{2}4~ a~ c$ 

Zeroes of the function (roots)
Name  Formula  Legend 
Zero point of homographic function  Show source$x=\frac{ b}{ a}$ 

Zero of the linear function  Show source$x=\frac{ b}{ a}$ 

Zero of the linear function from pointslope form  Show source$x= x_0\frac{ y_0}{ a}$ 

Zero of the linear function from constantslope form  Show source$x=\frac{ y_0\cdot\left( x_1 x_0\right)}{ y_1 y_0}+ x_0$ 

The first root of the quadratic function  Show source$x_1=\frac{ b\sqrt{ \Delta}}{2~ a}$ 

The second root of the quadratic function  Show source$x_2=\frac{ b+\sqrt{ \Delta}}{2~ a}$ 

Some facts
 The homographic function is a function that can be presented in the below form:
$y=\frac{ a~ x+ b}{ c~ x+ d}$where:
 $y$  function value (the function value at single point x, often marked as f(x)),
 $x$  function argument (called also independent value),
 a, b, c, d  homographic function coefficients (parameters defining concrete homographic function, c ≠ 0).
 The graph of the homographic function is hyperbola. To determine monotonicity of the homographic function, we can calculate its discriminant:
$D= a\cdot d b\cdot c$Then, depending on the value of the discriminant, the following scenarios are possible:
 the discriminant is negative (D < 0)  the function is decreasing,
 the discriminant is positive (D > 0)  the function is increasing,
 the discriminant is equal to zero (D = 0)  the function is reduced to the constant function.
 the discriminant is negative (D < 0)  the function is decreasing,
 In the general case, the homographic function has two asymptotes:
 horizontal asymptote given by the equation:
$y=\frac{ a}{ c}$  and vertical asymptote:
$x=\frac{ d}{ c}$
 horizontal asymptote given by the equation:
 A homogeneous function can have exactly one zero point or has no zeros at all. It depends on the coefficient b:
 if the coefficient b is different from zero (b ≠ 0)  the homographic function has exactly one zero point, its graph intersects OX axis at the point:
$x=\frac{ b}{ a}$  if the coefficient b equals zero (b = 0)  the homographic function has no zeros, its graph does not cross the OX axis.
 if the coefficient b is different from zero (b ≠ 0)  the homographic function has exactly one zero point, its graph intersects OX axis at the point:
 A special case of the homographic function is the function b/x (often called a/x, in this case formal parameter b is renamed to a):
$y=\frac{ b}{ x}$The b/x function has no zeros, and its symmetry point is origin of the coordinate system (point (0,0)).
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