Homographic function calculator
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#

BETA TEST VERSION OF THIS ITEM
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.
Feel free to send any ideas and comments !

# 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

# What do you want to calculate today?#

 Choose a scenario that best fits your needs I know function argument ($x$) and homographic function coefficients (a, b, c, d) and want to calculate function value ($y$)I know coefficient d (d) and coefficient c (c) and want to calculate vertical asymptote of homographic function (x)I know coefficient a (a) and coefficient c (c) and want to calculate horizontal asymptote of homographic function (y)I know homographic function coefficients (a, b, c, d) and want to calculate dicriminant of the homographic function ($D$)I know coefficient a (a) and coefficient b (b) and want to calculate zero of the function ($x$)I know function argument ($x$) and coefficient b (b) and want to calculate value of b/x function ($y$)

# Calculations data - enter values, that you know here#

 Function value ($y$)(the function value at single point x, often marked as f(x)) => Vertical asymptote of homographic function (x) => Horizontal asymptote of homographic function (y) => Dicriminant of the homographic function ($D$)(when D > 0 the function is increasing, when D < 0 the function is decreasing) => Zero of the function ($x$)(argument for which the function has a value of zero, its a solution of f(x) = 0 equation) => Value of b/x function ($y$)(the value of f(x)=b/x function for given x, parameters a,d are zero, parameter c is 1) => Function argument ($x$) <= Coefficient a (a) <= Coefficient b (b) <= Coefficient c (c) <= Coefficient d (d) <=

# Result: function value ($y$)#

Summary
Used formulaShow source$y=\frac{ a~ x+ b}{ c~ x+ d}$
ResultShow source$1$
Numerical resultShow source$1$
Result step by step
 1 Show source$\frac{1\cdot1+1}{1\cdot1+1}$ Multiply by one 2 Show source$\frac{1+1}{1\cdot1+1}$ Multiply by one 3 Show source$\frac{1+1}{1+1}$ Cancel terms 4 Show source$1$ Result
Numerical result step by step
 1 Show source$1$ Result

# 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.
• 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)).