Interactive Rational Functions & Transformations

This interactive tool allows you to explore rational functions of the form:

\[ f(x) = \frac{ax + b}{cx + d} \]

Adjust the coefficients, select mathematical transformations, and observe how the graph and asymptotes change dynamically.

How to Use This Tool

Set coefficients a, b, c, d using the input boxes below.
Click Update Graph to generate the baseline function.
Select a transformation from the dropdown menu (e.g., Reflections, Stretches).
Use the toggle switch to easily show or hide the transformed graph.
Use the zoom controls below to examine different coordinate regions.

Mathematical Note: The vertical asymptote occurs at \( x = -\frac{d}{c} \) (when \( c \neq 0 \)), and the horizontal asymptote occurs at \( y = \frac{a}{c} \).

Function Parameters

Coefficient a:

Coefficient b:

Coefficient c:

Coefficient d:

Original Function:

\[ f(x) = \frac{1}{x} \]

Apply Transformation

Show Transformed Graph:

Transformed Function:

\[ h(x) = \frac{1}{x} \]

Zoom Controls

Original Function: \( f(x) \)

Transformed Function: \( h(x) \)

Red dashed lines indicate vertical and horizontal asymptotes.