So we have right... What does this mean?
is a number. Think of in terms of the it take on values
Then is a mapping of It takes the values of and transforms them to take on new properties.
Again is just the Real line:
on the other hand, takes on the properties of a parabola. Also, it can only yield positive values, so its range is restricted to
So as we feed input values, it transforms them to take on these new properties as described above.
When we set equal to we are assigning a variable to the transformed values. So is a variable that is a function of