Understanding Graphing Functions - Advanced Algebra Lesson 1 Video

By: Guest More than a year ago

Very good presentation. I have a test tomorrow and this just reinforced what I have learned. VEry well explained! Woulda saved me hours of resorting to my book cus my teacher cant explain like you. Keep it up.

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By: Guest More than a year ago

Lamee.... Did not help me at all =/

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Understanding Graphing Functions - Advanced Algebra Lesson 1

Hi and welcome to the Advanced Algebra Tutor. In this course, we are going to continue where my other DVDs left off and continue on our path of Algebra and pretty much covering most Algebra that anyone would encounter. So I struggled a little bit with what to call this class because I titled it Advanced Algebra but I want you to know as we start off on this journey together that nothing in this class is really hard, okay. It has a title that sounds hard, Advanced Algebra, okay but nothing is difficult if it is explained in the right way so my goal is teach you everything step by step so that no topic sounds tough or intimidating or hard and we are going to do that by working example problems for every single topic here. Okay so just stick with me step by step and you will be able to do just fine. The other thing I want to say is that this class is kind of a little of a hodgepodge of things that I felt like people have requested over the years and that I felt like people should understand when going on and continuing their studies of Algebra. Things in this course are covered either in an Algebra III class. Sometimes there is a class called Algebra III depending on if you take that. Some of these topics are actually taught in Algebra II depending on the class that you take and the teacher that you have and all of these things are covered in a college Algebra class so if you are taking college Algebra, you are definitely going to need this DVD and also my other Algebra DVDs to ace that class and it is very comprehensive once we have those, okay. So let us just get started here, the title of this section, the first section here is called Graphs of Functions. In my previous DVDs; we talked about graphing lines, we talked about Y equals and X plus B and graphing a line and on the left hand side it is always Y equals something; x+b, your 3x+2 or y=5 or something and what we were doing there was we were creating a table of X values and Y values and we were plotting them and we were drawing lines mainly is what we were drawing and now we are going to expand our envelope into the realm of functions okay. So I want to dispel this myth with you right now. A function is very, very simple. A function is a fancy word that just means Y equals something, okay so instead of saying of y=3x+2, you have a function that you define that equals 3x+2. It is just a new word for the same thing that you already know, and we are going to see that right here. So lets just get started and I will write a definition on the board. I am not going to write too many definitions in this class but I am going to do it here. A function which is a term that you really need to know and we are going to denote this function; F of X, this is not F times X; parenthesis here does not mean multiplication, it is F of X and I will explain what that means in a minute. All this thing does is it takes an input and the input is X, that is why it is F of X, it is taking an input, we call that X and this is my terminology here. It spits out, I am actually going to write this here, spits out another value and we call that other value, F of X. So this is exactly what it is, it is a function. I do not know why exactly they call it a function and I guess you could probably say that it performs some function on some values of X and it is kind of like this box, okay. A function is kind of like a box, just imagine this empty box, you have no idea what is inside of it, but we label it F of X. We take the values N and these values are X and by the way you know, we have a lot of letters here and these are just values. X could be one, X could be two, X could be 25, X could be 1.5, X could be 1.9, whatever. Any number you want, put it in this thing and into this box and inside of here is some mathematical gears, we will look at some functions and show you what they look like but it is something that changes these input values and it dumps out some different output values and we call these values F of X. It means F which is a function had operated or has you know, otherwise messed with these values of input X and you get some new values out, so you might put one on the input here and you might get seven on the output. You might put two on the input here and you might get, 39 on the output, whatever. And F of X is just some mathematical equation that describes what happens to the input and transforms it into the output. So, F of X which we will look at all day here, that is actually the mathematical beast that takes the input and changes it into the output. Now, this is no different than what you already know from my other DVDs and also introductory Algebra. F of X; they just called it Y. Okay, that is all, so when you were dealing with equations of lines, you had something like Y is equal to 3x+2. This is exactly the same thing as the function F of X is equal to 3x+2. You see this is why I get frustrated with Math, History, and textbooks because they spend all of this time teaching you Y equals 3x+2, you will finally understand that you put a value of X in and you get a value of Y out, multiply, times three, add two and get the value of Y and you understand this finally. You understand that you put a value of X in, you will get a value of Y. And then one day, you turn the page and they talk about functions F of X and the students think that this going to be something totally different because my goodness, why would they put another section in the book if it was not the same thing. It is exactly the same thing, this is no different, this is just taking a value of X in which is all you were doing here; you are putting a value of X in. Put a value of X in, it goes right into here, multiply and add and the value of F of X that you get out is just the same thing as Y, it is just a new label, it is just that when you start to get up higher in Algebra, they like to call it a function so that it is kind of more directly kind of describes what was happening, the function operates on the variable X and returns something else, you just call it F of X because it is operating on X. So, this is no different than what you have seen. A function is just a box, it takes some numbers in, changes them, multiplies, divide, you might takes square root, you might do some other stuffs in here and the values you will get on the output are just your values of Y, that what you use to deal with. We just call them values of F of X because we are talking about the fact that it is a function. Now, look at our definition, a function F of X takes and input X and it spits out another value and we call it F of X and this is the output here, that is what we are interested it. You can graph these just like you can graph back when you learned how to graph y=3x+2. The way you would graph this is, you will have your values of X here and in the other DVD course and also in your introductory textbook, we would put Y up here and I would show you, look, this is a coordinate system. You have values of X that go this way; one, two, three, four, five, six, seven, eight, nine, 10 or whatever and you will have values of Y that go this way; one, two, three, four, five, six, seven, eight, nine, 10 or whatever, and you also have your negative values of Y and you also have your negative values of X and they go on forever and ever. And I would tell you that and you would nod your head and say okay, great and then we talk about, what we can graph here okay. There is no difference from what you have already learned in talking about this functions, okay. Instead of putting a Y up here in this axis, I am just going to put F of X, okay that is all we were doing. Because do not forget, F of X is just a function, you stick some number in there and you get another number back, it is the same thing Y was doing for you. It is just a different label. So this axis here is called the X axis and this axis is called the F of X axis which is what you would graph there and so when you put X=0 in and you might get zero and you might get a graph, you could draw a graph, it might look like something like this. As X increases over here, F of X might get higher and then after a certain po

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Hi and welcome to the Advanced Algebra Tutor. In this course, we are going to continue where my other DVDs left off and continue on our path of Algebra and pretty much covering most Algebra that anyone would encounter.

So I struggled a little bit with what to call this class because I titled it Advanced Algebra but I want you to know as we start off on this journey together that nothing in this class is really hard, okay.

It has a title that sounds hard, Advanced Algebra, okay but nothing is difficult if it is explained in the right way so my goal is teach you everything step by step so that no topic sounds tough or intimidating or hard and we are going to do that by working example problems for every single topic here. Okay so just stick with me step by step and you will be able to do just fine.

The other thing I want to say is that this class is kind of a little of a hodgepodge of things that I felt like people have requested over the years and that I felt like people should understand when going on and continuing their studies of Algebra.

Things in this course are covered either in an Algebra III class. Sometimes there is a class called Algebra III depending on if you take that. Some of these topics are actually taught in Algebra II depending on the class that you take and the teacher that you have and all of these things are covered in a college Algebra class so if you are taking college Algebra, you are definitely going to need this DVD and also my other Algebra DVDs to ace that class and it is very comprehensive once we have those, okay.

So let us just get started here, the title of this section, the first section here is called Graphs of Functions. In my previous DVDs; we talked about graphing lines, we talked about Y equals and X plus B and graphing a line and on the left hand side it is always Y equals something; x+b, your 3x+2 or y=5 or something and what we were doing there was we were creating a table of X values and Y values and we were plotting them and we were drawing lines mainly is what we were drawing and now we are going to expand our envelope into the realm of functions okay.

So I want to dispel this myth with you right now. A function is very, very simple. A function is a fancy word that just means Y equals something, okay so instead of saying of y=3x+2, you have a function that you define that equals 3x+2. It is just a new word for the same thing that you already know, and we are going to see that right here.

So lets just get started and I will write a definition on the board. I am not going to write too many definitions in this class but I am going to do it here. A function which is a term that you really need to know and we are going to denote this function; F of X, this is not F times X; parenthesis here does not mean multiplication, it is F of X and I will explain what that means in a minute. All this thing does is it takes an input and the input is X, that is why it is F of X, it is taking an input, we call that X and this is my terminology here. It spits out, I am actually going to write this here, spits out another value and we call that other value, F of X.

So this is exactly what it is, it is a function. I do not know why exactly they call it a function and I guess you could probably say that it performs some function on some values of X and it is kind of like this box, okay. A function is kind of like a box, just imagine this empty box, you have no idea what is inside of it, but we label it F of X.

We take the values N and these values are X and by the way you know, we have a lot of letters here and these are just values. X could be one, X could be two, X could be 25, X could be 1.5, X could be 1.9, whatever. Any number you want, put it in this thing and into this box and inside of here is some mathematical gears, we will look at some functions and show you what they look like but it is something that changes these input values and it dumps out some different output values and we call these values F of X. It means F which is a function had operated or has you know, otherwise messed with these values of input X and you get some new values out, so you might put one on the input here and you might get seven on the output. You might put two on the input here and you might get, 39 on the output, whatever. And F of X is just some mathematical equation that describes what happens to the input and transforms it into the output. So, F of X which we will look at all day here, that is actually the mathematical beast that takes the input and changes it into the output.

Now, this is no different than what you already know from my other DVDs and also introductory Algebra. F of X; they just called it Y. Okay, that is all, so when you were dealing with equations of lines, you had something like Y is equal to 3x+2. This is exactly the same thing as the function F of X is equal to 3x+2. You see this is why I get frustrated with Math, History, and textbooks because they spend all of this time teaching you Y equals 3x+2, you will finally understand that you put a value of X in and you get a value of Y out, multiply, times three, add two and get the value of Y and you understand this finally. You understand that you put a value of X in, you will get a value of Y.

And then one day, you turn the page and they talk about functions F of X and the students think that this going to be something totally different because my goodness, why would they put another section in the book if it was not the same thing. It is exactly the same thing, this is no different, this is just taking a value of X in which is all you were doing here; you are putting a value of X in. Put a value of X in, it goes right into here, multiply and add and the value of F of X that you get out is just the same thing as Y, it is just a new label, it is just that when you start to get up higher in Algebra, they like to call it a function so that it is kind of more directly kind of describes what was happening, the function operates on the variable X and returns something else, you just call it F of X because it is operating on X.

So, this is no different than what you have seen. A function is just a box, it takes some numbers in, changes them, multiplies, divide, you might takes square root, you might do some other stuffs in here and the values you will get on the output are just your values of Y, that what you use to deal with. We just call them values of F of X because we are talking about the fact that it is a function.

Now, look at our definition, a function F of X takes and input X and it spits out another value and we call it F of X and this is the output here, that is what we are interested it. You can graph these just like you can graph back when you learned how to graph y=3x+2. The way you would graph this is, you will have your values of X here and in the other DVD course and also in your introductory textbook, we would put Y up here and I would show you, look, this is a coordinate system. You have values of X that go this way; one, two, three, four, five, six, seven, eight, nine, 10 or whatever and you will have values of Y that go this way; one, two, three, four, five, six, seven, eight, nine, 10 or whatever, and you also have your negative values of Y and you also have your negative values of X and they go on forever and ever. And I would tell you that and you would nod your head and say okay, great and then we talk about, what we can graph here okay. There is no difference from what you have already learned in talking about this functions, okay.

Instead of putting a Y up here in this axis, I am just going to put F of X, okay that is all we were doing. Because do not forget, F of X is just a function, you stick some number in there and you get another number back, it is the same thing Y was doing for you. It is just a different label. So this axis here is called the X axis and this axis is called the F of X axis which is what you would graph there and so when you put X=0 in and you might get zero and you might get a graph, you could draw a graph, it might look like something like this.

As X increases over here, F of X might get higher and then after a certain po

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