Working with a function or equation, we often need to change or modify it. Changing a
function or equation, we can do it changing its curve. And changing it, we change its
location or its form. Why change though?

Doing problems with functions or equations, we often need to change them so that we
can get the ones we want, and can get them readily and fast enough. And changing
functions or equations, we say we do transformations to them, and say we do function
transformations or equation transformations. And doing it, we do it changing its curve,
that is, its graph. So we can call it a graph operation.

In GRAPH OPERATIONS, discussions will be focused on how to change functions or
equations changing their curves. So this book is about curves. And more specifically,
what's covered here is how to put a curve in a graph many different ways. So you will
get to see in this book, how to move, change or alter, or modify a curve, and how to get
the equation of the curve changed, that is, the new equation. And you will get to see also,
how to keep track of the variables used in the equation or function when it is getting
changed.
So we don't just do matrix applications to get a new curve or a new equation or function.
We approach transformations pragmatically rather than theoretically. So you will get to
see what actually changes and how changes are made or happen. Why though?

As mentioned above, doing problems with functions or equations, we often need to
change them so that we can get the solution readily and fast enough. And it is
particularly the case, when we do calculus. Doing it, we often need to manipulate curves
so that we can see how to approach solutions to problems with functions or equations.
We do need to do so not only finding derivatives or integrals but understanding rules or
theorems, too.

Putting curves many different ways, we can often see better how to get the solutions
more readily and faster. We can have many problems where having only to put curves in
graphs, we can see the solutions right away. And also, there are many problems we can
solve only if we know how to manipulate curves as well as how to construct the graphs.

What we actually do solving a problem is in fact, putting the problem many different
ways. That is, putting a problem many ways, we get to see the solution. And also, not
just reading the problem but actually looking at the problem, too, we can see better the
solution's whereabouts. And actually looking at it, we put it in a graph. And some
sample pages are at: http: //www.runmath.com/ExcerptFromGraphOpSeongKim.pdf