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Mercyhurst UniversityDept of Math and ITDr Williams Home

Function Transformations


Function:    

\( f(x) = x^2 \)
\( f( \)\( x \)\( ) \)

Value of A: 1


Value of B: 1


Value of C: 0


Value of D: 0

About Function Transformations

Starting with the graph of a function \(f(x)\), the graph of \[ A f(Bx - C) + D \] is obtained by stretching the graph of \(f\) vertically by a factor of \(A\) and horizontally by a factor of \(B\), while translating it vertically by a factor of \(D\) and horizontally by a factor of \(C\).

Using the Applet

This applet allows you to adjust the parameters of the function \( A f(Bx - C) + D \), where \(f(x)\) is a quadratic, cubic, linear, or floor function. Choose a function type to transform from the drop down menu. Then, use the sliders to adjust the values of \(A\), \(B\), \(C\), and \(D\) to see how the graph changes. The transformed graph will be displayed in black. The blue dots show the original function.

About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.