Transformation of Functions
Transformation of functions involve moving a function around so that is can be recognized as a simpler function. A lot of seemingly complex equation are really just simple shapes with a few simple transformations! This is especially true with polynomials and trigonometric functions. You can see more about this; Transformation of Functions
So you have finished some basic high school math, now you must do calculus. It is a little intimidating at first, but you should know that pre-calculus is studied first, before getting into things you have not seen before. Pre-calculus can mean many different things, depending on where it is studied. Typically though pre-calculus is a study of all the skills required to do differential, integral, vector, and advanced calculus.
Pre calculus really is not that difficult, it is mostly just a review of algebra stuff. There will be a lot of functions and simple math problems. The main sections of pre calculus (function studies and limits) will be covered thoroughly.
A limit could exist, this depends really depends if the function goes to the same value from both sides of the graph. Limits are an essential part of calculus and are used to form the definition of the derivative. Limits are also used to determine the behavior of a function at discontinuities and infinite points.
We are not really concerned with the limits stuff, but it is a really important part of pre calculus. We are more concerned with transformation of functions. There are three different types of transformations; reflections, scaling, and translations. Reflections involve flipping the graph in different directions. Scaling changes the size and the shape in both direction. Translations move the graph. It is really as simple as that! There are a bunch of rule and recognition point to go along with that but that really isn't that important right now. Just know that transforming functions can make hard function a lot easier to deal with. Since we can see them for simple equations instead of messy ones.
So you have finished some basic high school math, now you must do calculus. It is a little intimidating at first, but you should know that pre-calculus is studied first, before getting into things you have not seen before. Pre-calculus can mean many different things, depending on where it is studied. Typically though pre-calculus is a study of all the skills required to do differential, integral, vector, and advanced calculus.
Pre calculus really is not that difficult, it is mostly just a review of algebra stuff. There will be a lot of functions and simple math problems. The main sections of pre calculus (function studies and limits) will be covered thoroughly.
A limit could exist, this depends really depends if the function goes to the same value from both sides of the graph. Limits are an essential part of calculus and are used to form the definition of the derivative. Limits are also used to determine the behavior of a function at discontinuities and infinite points.
We are not really concerned with the limits stuff, but it is a really important part of pre calculus. We are more concerned with transformation of functions. There are three different types of transformations; reflections, scaling, and translations. Reflections involve flipping the graph in different directions. Scaling changes the size and the shape in both direction. Translations move the graph. It is really as simple as that! There are a bunch of rule and recognition point to go along with that but that really isn't that important right now. Just know that transforming functions can make hard function a lot easier to deal with. Since we can see them for simple equations instead of messy ones.
