Category: High School Calculus

Understanding Domain and Range Part 1

College Algebra, High School Calculus, High School Mathematics

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

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Guest Post: Derivatives and an Introduction To Calculus

High School Calculus, High School Mathematics

by Shaun Klassen

One of the mathematics subjects most feared by students is the “dreaded” differential calculus subject.  Absolutely, it is more complicated than more common basic algebra that most would have studied up to this point.  And of course, to work with calculus, one must be familiar with all of the earlier concepts that build up a strong mathematical foundation, including things like algebra, trigonometry, and graphing.  However, this is not to say that calculus has to be hard, or “impossible.”  It is completely doable if you start slowly by learning the general problem solving strategies.  In this guest post, I want to introduce the main concept of differential calculus – the derivative – and I encourage you to visit my math website to find out much more information about this subject.

The name “differential calculus” is a descriptive one – it is based on differences, or changes.  More specifically, it is all about describing how one quantity changes with respect to another one, or in other words, the rate of change.  The derivative is used to express this function, but let’s examine this concept a little more closely by considering everyone’s favourite rate of change: velocity.  » Read more

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The 0.0001 Time Rate Approach

High School Calculus

by Armand Gelig Macapagong

I encountered Differential Calculus when I was in my 2nd-year High School. As a part of the Math Magi, a Mathematics club in our school, we were taught advance topics apart from our daily Math subjects in class. One of these was an introduction to Differential Calculus. I found Differential Calculus as one of the interesting subjects and my favorite topics were L’Hospital’s rule and Maxima-Minima.

When I went to college, I encountered Differential Calculus again. This time, it becomes a lot easier since I already had a taste of this subject. But what caught my attention was that, a lot of students in our class failed in almost all quizzes. This brought me to thinking, that if I can introduce an easier concept to my classmates, or if I can develop a less complex approach which they can easily grasp, maybe I can help them. So I worked hard in finding an easier approach. I developed this technique two years after that Differential Calculus subject. So, I never really had the chance to help my classmates back then. » Read more

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