Linear fractional transformation

Okay, so imagine you have a toy car and you want to transform it into a different toy car. Now let's say you have a magic wand that can stretch and shrink the toy car, turn it around, and move it to a different place all at the same time. This is kind of like what a linear fractional transformation does, but with numbers instead of a toy car and a magic wand.

Linear fractional transformations are like special rules for taking a number and turning it into a different number. These rules can do things like stretch the number out, squash it down, rotate it, or move it around on a number line. They work kind of like a magic wand that can transform numbers into different numbers in special ways.

One cool thing about linear fractional transformations is that they are made up of simple math operations like dividing and adding. So you don't need a magic wand or anything fancy to do them - you just need to know how to divide and add up numbers!

Overall, a linear fractional transformation is just a fancy way of saying a rule for transforming numbers. By using these rules, we can stretch, shrink, rotate, and move numbers around on a number line in special ways.