Understanding Domain and Range Part 2

In the previous post, we have learned the graphical representation of domain and range. The domain of the function f is the shadow or projection of the graph of f to the x-axis (see the red segment in the figure below). The range of f is the projection of the graph of f to the y-axis (see the green segment in the figure below). In this post, we are going to learn how to analyze equations of functions and determine their domain and range without graphing.

domain and range

If a graph of a function is projected to the x-axis, the projection is the set of x-coordinates of the graph. A single point (a,0) on the projection means a point on the graph exists. The existence of a point implies that f(a) exists. This means that the function is defined at x = a. In effect, the domain of a function is the set of x-coordinates that makes the function defined. In what follows, we learn some examples to illustrate this concept.  » Read more

Understanding Domain and Range Part 1

The domain of a function is the set of x-coordinates of the points in the function. The range of the function f is the set of y-coordinates of the points in the function. So if we have a function f with points (-3, -2), (-1, 3), (2, 3), and (5,4), then the domain of the function f is the set {-3, -1, 2, 5} and the range of f is the set {-2, 3, 4). Graphically, we can say that the domain is the  “projection” of the points to the x-axis (see red points in the following figure).

domain

The range of f is the projection of the points to the y-axis (see green points in the following figure).  » Read more

Book Review: The Humongous Book of Calculus Problems

I bought this book a year ago as a refresher of Calculus and as of now, I am almost finished reading it. I think what separates this book from the rest are the numerous worked examples (well, 1000 of them) with detailed solutions and explanations. Additional pointers and explanations in layman’s words are provided as notes.

This book has 565 pages containing 28 chapters. The first 8 chapters contain a review about equations, polynomials, functions, and trigonometry, while the remaining chapters discussed topics in Calculus I and II: Limits, Differentiation, Integration, Parametric and Polar Equations, Sequences and Series. As a bonus, a chapter on Differential Equations is also included.  » Read more

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