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 transformations, and observe the changes on the graph.

How to Use This Tool

  1. Set coefficients a, b, c, d using the input boxes above
  2. Click Update Graph to see the function
  3. Select a transformation from the dropdown menu
  4. Use the toggle switch to show/hide the transformed graph
  5. Use zoom controls to examine different regions
  6. Click Reset View to return to default view

Note: Vertical asymptote at \( x = -\frac{d}{c} \) (when \( c \neq 0 \)), horizontal asymptote at \( y = \frac{a}{c} \).

Function Parameters

Original Function:

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

Function Transformation

Show Transformed Graph:

Transformed Function:

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

View Controls

Original Function: \( f(x) \)
Transformed Function: \( h(x) \)

Red dashed lines indicate asymptotes