This book is about functions, and covers basic functions of all kinds, which include composite functions, inverse functions, some exponential and log functions, periodic functions as well as ordinary algebraic functions.
And all those are covered not only in one book but in two partial books, too.
The two partial books are as follows:
ALGEBRA EXAMPLES BASIC FUNCTIONS 1
(It covers all the basics on functions and composite functions.)
ALGEBRA EXAMPLES BASIC FUNCTIONS 2
(It covers inverse functions, exponential and log functions, and periodic functions.)
And both are available at amazon.com
So clear will be what functions are about and how they mingle with algebra. And you will get to see them through examples, with solutions detailed, of course, so that you can get along with the book yourself, and your math can run not only properly but fast enough, too.
Why functions, though?
Using functions, we can see how things change.
More specifically, how values change as other values change. How come?
Basically, functions are about values that change.
Expressing values, we use numbers, of course.
Not only that, of course. But we use letters, too, called variables or constants.
And using those letters, along with numbers, we make expressions that express values.
So values of expressions change as values of variables change.
And we want to know how their values change as values of their variables change.
And we call such an expression a function.
So we want to know how the value of a function changes as the value of the variable changes.
And thus, doing physics, economics, or anything that have to do with changes, we want to know about functions. In short, how things change.
Increase or decrease
Going up or coming down
Speeding up or slowing down
So how fast or slow is it? And by how much or how many?
For instance:
How the distance changes as time changes.
How the pressure changes as temperature changes.
How the price changes as supply decreases or demand increases.
And after all, how outputs change as inputs change.
Functions get inputs as time, and in return, produce outputs as distance.
So if need to work with things change, you want to know functions, and how they work, together with how to work with them.
And functions are expressions mainly made of polynomials, made of variables, constants, and numbers, of course.
So you want to know polynomials, how they work, and how to work with them, too.
And as stated above, polynomials are expressions made of variables, constants, and numbers, of course.
You want to know thus, variables and constants, how they work, and how to work with them, along with their arithmetic. What then, about numbers?
Numbers of all kinds, of course
Mainly though, we work with numbers said to be real. So at least, you want to know real numbers of all kinds: integers, rational numbers, and irrational numbers.
And we have numbers that have different looks.
Among those, we often use powers, and have logarithms, called logs, too, no other than exponents though. And that's not it. We have radicals, called roots, too.
And using those above, we can make expressions called functions.
So you want to cover quite a few to learn, make, and use functions.
And we can actually see how functions behave, too.
Each function can have its own look, which is called its curve.
So putting the curve in a place called a graph, you can see readily and fast where the one you are always busy looking for is.
It is of course, the solution to the problem you are always busy doing.
More information on the books can be found at:
http://www.runmath.com/BooksPrinted.htm
