Graphs Transformation

Pls click on the above pics for the full size

Also pls note that the order of TSRRST is also applicable for both the forward & backwards....meaning for eg. (backwards) to get y=f(x) from y=D + Cf (Bx + A), we will still start wif translation (T) ferst in the brackets by getting rid of A first by forming the eqn y= D + C f(Bx + A -A). Hence, the order still follows just that everything is by eliminating the form to get back y=f(x).

How to remember what sort of transformation to do?

Simple, always remember that those transformation along the x-axis or those that are in the brackets are always opposite of wat they meant. For eg in translation, y=f(x + a) means a translation of a units in the negative x-axis direction (to the left by a units // to x-axis) while y=f(x-a) means a translation of a units in the positive x-axis direction (to the right by a units // to x-axis).

For scaling involving the x-axis it is always a reciprocal of the number. For eg, y=(2x) will mean a scaling along the x-axis by 1/2 times. If its y=(Bx), it will be a scaling along the x-axis by 1/B times meaning multiply the x-coordinates by 1/B. For reflection involving the numbers in the bracket like y=(-x), it means a reflection about the y-axis. In summary, it can be noted that any transformation in the bracket is always the opposite of what is meant (for translation), a reciprocal of the number (for scaling) & about the opposing axis (for reflection). Simply put, anything in the brackets is about OPPOSITES.

For those transformation involving outside the brackets or involving the y-axis are quite straight forward because they are usually written to be exactly what it means. For example a translation of y=f(x) + a means a translation of a units in the positive y-axis direction (move up) n the reverse for y=f(x) - a means a translation of a units in the negative y-axis direction (move down). For scaling, there is NO RECIPROCAL FORM NEEDED, when it is written as y= 2f(x), it simply means scaling of factor of 2 units along the y-axis meaning just multiply the y-coordinates by 2 NOT 1/2! Only reflection still follows the general rule of being the opposite whereby y=-f(x) actually means a reflection about the x-axis. Simply put, anything out of the bracket is straight forward and is all involving the y-axis EXCEPT for REFLECTION!!!

After mastering the transformation for graphs, it becomes quite standard for questions involving graphs transformation. Just ensure that there are no carelessness.