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Precalculus Review - Intro

In mathematics, precalculus is the study of functions (as opposed to calculus, which is the study of change, and algebra, which is the study of operations and their application to solving equations). It is generally considered to be a part of mathematics that prepares students for calculus.

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Glam F.

April 20, 2021

Find values of x, if any, at which f is not continuous. f(x) = 5x^4 - 3x + 7 f(x) = 3 squareroot x - 8 f(x) = x + 2/x^2 + 4 f(x) = x + 2/x^2 - 4 f(x) = x/2x^2 + x f(x) = 2x + 1/4x^2 + 4x + 5 f(x) = 3/x + x - 1/x^2 - 1 f(x) = 5/x + 2x/x +4 f(x) = x^2 + 6x

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Video Transcript

So we get to now learn about one of the coolest areas in all of science, and that is calculus. And you may say, Well, why haven't I learned about this before now? And that's a great question. And the reason is quite simple, because calculus, even though a lot of the concepts are very simple and easy to grasp, the actual process of solving problems is very difficult. And I'll say this again. But I'm going to write it for you now because I believe it is very important to hold on to, and that's this. The hardest part I have Calculus is not calculus but algebra. So you have spent most of your life learning algebra. You learned a little bit of arithmetic. Growing up, he learned some algebra, and now you are ready to basically take everything that you have learned from algebra, put it together and actually do something with it. To start answering the question. What is the point of learning all of this? So before we jump into the calculus itself, we're going to spend some time reviewing algebra or reviewing topics from pre calculus. And so some of these ideas are pretty simple. Some of them are a little bit more difficult, but we really do need to pull from everything. So we're gonna talk about things like functions. We're gonna talk about things eso specific types of functions. So trig and metric functions. That's always a fun one. What else are we going to talk about? We're going to talk about polynomial functions. We're gonna talk about exponential functions because all of these functions are going thio going to play a big part when we start trying to model the real world and using calculus too break down and understand and analyze the functions that we're using toe model, the real world. So it's very important that we have a grasp and and the more time that you spend thinking about functions thinking about the subtleties of functions, thinking about, you know, how are the trig and metric functions really defined? Where they coming from naturally, how? How, how the polynomial show up in nature, What is it about exponential functions that make them so important? The more you start to grapple with those questions, the more you're really going to appreciate the beauty and subtlety that is calculus