Calculator helpful during common operations related to homographic function such as calculating value at given point, calculating discriminant or finding out function asymptotes.

Beta version#

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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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Some facts#

The homographic function is a function that can be presented in the below form:

$y=\frac{a \cdot x+b}{c \cdot x+d}$
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.
In the general case, the homographic function has two asymptotes:
- horizontal asymptote given by the equation:
  
  $y=\frac{a}{c}$
- and vertical asymptote:
  
  $x=\frac{-d}{c}$
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.
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)).

Tags and links to this website#

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homographic_function_calculator · homographic_function_roots_calculator · homographic_function_value_calculator · homographic_asymptotes_calculator · homographic_vertical_asymptote_calculator · homographic_horizontal_asymptote_calculator · value_of_homographic_function_in_point · homographic_discriminant_calculator · hiperbola_calculator · calculator_of_hiperbola_root · calculator_of_hiperbola_asymptotes · calculator_of_vertical_hiperbola_asymptote · calculator_of_horizontal_hiperbola_asymptote

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What tags this calculator has#

CALCULATOR · MATH · A -> Z (all)

Permalink#

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https://calculla.com/homographic_function_calculator?ioIntentSchemeId=intent0&functionValue=$symbolic(1)&functionArgument=$symbolic(1)&homographicParameterA=$symbolic(1)&homographicParameterB=$symbolic(1)&homographicParameterC=$symbolic(1)&homographicParameterD=$symbolic(1)&homographicParametersABCD=$symbolic(1)&homographicAsymptoteVertical=$symbolic(1)&homographicAsymptoteHorizontal=$symbolic(1)&homographicDiscriminant=$symbolic(1)&root=$symbolic(1)&homographicValueBPerX=$symbolic(1)

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