Translations of functions can really change how their graphs look, and it's fascinating to see how it all works.

When we study translations in year 12 math, we're mainly looking at how the graph moves along the x-axis (side to side) or the y-axis (up and down).

1. Horizontal Translations:

• If you have a function called ( f(x) ) and you change it to ( f(x - a) ), the graph moves to the right by ( a ) units.
• On the other hand, if you change it to ( f(x + a) ), the graph shifts to the left by ( a ) units.

2. Vertical Translations:

• For vertical shifts, if you take your function ( f(x) ) and modify it to ( f(x) + b ), the whole graph moves up by ( b ) units.
• If you write it as ( f(x) - b ), then the graph moves down by ( b ) units.

Understanding these translations is really helpful when you want to draw graphs quickly. It’s amazing how just moving the graph can change how we see a function, like moving a curved line or a wave! This makes analyzing functions much easier and more fun to look at.