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Title: College Algebra: Exploring Functions, Part 3
Book Description: In part 3 of Exploring Functions, we explore operations on functions. We are familiar on the operations on real numbers: addition, subtraction, multiplication, and division. Since the output of a function is a real number, it is natural to think of applying these operations to functions.
We also illustrate dynamically a new operation: composition of functions. This new operation leads us naturally to consider the concept of inverse functions. After this, we begin an approach to the derivative concept by exploring the Rate of Change of a function. In particular, we discuss a very important concept that tells us more about the nature of the functions we encounter.
As we know, a function f relates two variables x (the independent) and y (the dependent) in a way that, for each x, there is a unique y such that y = f(x). Generally, as x varies, so does y. A question of profound importance is: how exactly does y change with x? The notion of rate of change gives a way to study this question.
The book finishes with some illustrations of various sorts of symmetries that functions may have.
Author: Samad Mortabit
Contained
in College Algebra Course. (Lab 4)
Suggested Use: College algebra or Precalculus level introduction to functions. Explanations are under the exclamation point (!) buttons.
Topics: College Algebra, Function, Function Composition, Graphing, Relations, symmetry, rate of change, composition of functions
Number of Pages: 6
Animation: Yes
Grade
Level: 