This book is for young students Gifted or Advanced in math. 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
About the Author: Knowing a little about math, but doing much about it, and trying to do more More importantly, doing a lot about math education, and trying to do much more So I enjoy helping students with math, and always find myself having lots of fun developing content in math education, and coming up with those contents that do help students get the concepts of math objects, and improve their skills, particularly in algebra and geometry, so that they can get solutions properly and fast enough. And more importantly, I enjoy watching students growing their interest and confidence in math as they make achievement learning and doing math. Math educational career of over 20 years. Working for students with various academic strengths and in various learning levels Implementing forward thinking processes Dedicated to student's math education and interaction with the parents or guardians. Ample experience in writing math books, providing instructions and training solutions which not only enhance the math skills and senses but promote and grow confidence in math Specialized in Developmental or Remedial and Special Math Education: - Developing and producing examples so that the students can take STEPS to get the ideas. - Showing students the examples so that they can come up with THEIRS and can approach the concept of the math object or math ideas as numbers, ratios, rates, powers or exponents, equations, formulas or identities, graphs, angles, lines, polygons, etc. - Encouraging or inducing the students to produce examples so that they can speed up or find other ways getting the solutions to the problems with the math objects they are learning, and they can grow CONFIDENCE and INTEREST. - Helping them thus, get to see THEMSELVES what they are learning, what it is about, how it gets made, how it works, and what they can do about it or with it. In short, students can get the meanings of math items they learn, and grow their math so that they can work with or use them PROPERLY and can get solutions FAST ENOUGH. M.S. Math. Rensselaer Polytechnic Institute B.S. Math. Michigan Tech. Univ.
