Numbermagic

This is the second part of my Graphs Blog. The first part showed how to convert Graphs to Equations. One important thing which I would like to add before I start the Blog, is that most Graphs do not not have a particular Equation, or equations for that matter, as in most graphs can't be limited to a few equations, but the equations can be found to plot the graphs very accurately. There are many techniques involved in the art of graphing :  1) Shifting  - There are two types of shiftings, related to graphs. One is shifting the x axis, and the other shifting the y axis.      Given a function y = f(x), we have to find a function y = g( ), such that the graph is shifted by k units to the right. Thus, we have x + k =  . f(x) = g( ), as the value of y will be constant, as only the x axis shifts. Therefore,                               f(x) = g(x + k)         ...

Graphs (2 D) are pretty cool, because they show us how a function, no matter how complicated, behaves over an interval. We can see how a function, which looks super complicated on a piece of paper beautifully unfolds itself, into a picture, and it is then, super easy to decipher the meaning of the function. In this Blog, I will discuss how to convert an equation to a Graph. Converting an equation to a graph is a very useful skill, because it helps to understand the function you are working with. It is also pretty fun. But, before that, it is essential to Understand the Concept of Maxima and Minima.  The maxima is a point on a curve, such that it has a higher value than the points near it in a close range. The minima is a point on a curve, such that it has a lower value than the points near it in a close range. Given a function y = f(x), the value of x, such that it's derivative at that point is 0, gives either a maxima, or a minima of the function. Though, there are some cases wher...