Transformations of Functions

This applet investigates simple transformations of general functions in the form f(x).

Author and programmer: Ron Barrow

UK Years 10-12, KS4, KS5, Higher GCSE Mathematics, Grades A*-A, Algebra and Graphs, OCR Edexcel AQA MEI C1 C2
US Grade 11, Grade 12 - Algebra - Pre-Calculus

   
           

Instructions below    See also:   Sin, Cos, Tan Transformations    Graph Recognition

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How to Use this Applet

The screen above is designed to help you continue your study of functions, by investigating their behaviour. There are seven functions for you to study. You can choose which function you want to look at from the drop-down list at the top of the screen. You don't have to know what these functions are, because their behaviour is similar for all functions of similar type.
There are eight different transformations to investigate with each function, and you can choose these by clicking the little circles at the bottom of the screen.

They are:
f(x) → f(x) + a, f(x) → f(x + a), f(x) → af(x), f(x) → f(ax)
f(x) → -f(x), f(x) → f(-x)
The last two are are only for age 16 - 19 students (A Level)
f(x) → |f(x)|, f(x) → f(|x|)
What happens in each case when you vary the value of "a"? The white line is the original function. The yellow one is the function after it has been transformed.
Investigate for yourself and have fun!