GRÁFICO DE UMA FUNÇÃO DO PRIMEIRO 1º GRAU - FUNÇÃO AFIM - AULA 5

Guys, are you studying the AFIM function and have questions about how to build the graph of this function? So follow Gis's class until the end because I'm going to explain all the details of how to build this graph, let's go? So welcome to another class on the Gis channel, take the opportunity to subscribe to the channel if you are not yet subscribed and leave a thumbs up.

And let's build the graph of the function that I brought to you today, the function is 4x - 8, let me say something here first before we start, this construction gets much more interesting, right, but understandable, let's say like this, when we get a situation of our daily life, our daily life and we transform this situation here into a graph, you know, the behavior of this function because so when I build a graph of an AFIM function, I can see it in more detail, I can see the information about the behavior of this function, okay? but here, as I want you to learn exactly how to build, let's talk about a more technical part, right, about construction, I already brought the exercise ready, just build the graph ready then be sure to watch the next classes and then I'll bring you an exercise which is contextualized and then we take this contextualized exercise and build the combined graph because then you've already learned the techniques properly, so I'm going to do the construction in two ways, okay, you choose the one you understand best, I always like it to show you several ways to choose, then you understand, right? So the first way might be longer, I don't know, let's go, I'll take it then and I'll build a table here so I'll build a table, one column will be the values ​​of x and the other column will be the values ​​of the function of f of x which is ours function, remember independent dependent variables and dependent variables, remember our variables, right?

Guys, you can see that I already put the values ​​of one, two and three here for X, but why did I already put these values ​​because I chose these values you can put any value you want, any value you put here for x, you find the value for the function and from there you can build the graph, okay, but what's my advice to you guys, let's be consistent, let's choose values ​​for X that are here or close here, right in this region here because otherwise it will be very far away, imagine you choose 50 for the X, then you will have to draw your You'll see later, so when you choose, always take the values ​​here that are kind of close, a negative, a zero, ok, combined like this, so let's start the function is 4 times which means that I 'm going to have to take my function and in place of this Watch this class then you will understand everything I'm saying here so I'm going to change that value of x 1 are 4, 4 - 8 will be minus 4 so when I change the X by 1 my function will be - 4 okay now I'm going to change the giving 4 x 2 are 8, 8 - 8 are 0 again when I change the so here it will be 4, ok, why did I only choose three points, I can't choose to put more values ​​here so you can do as many values ​​as you want, but for me to determine a straight line I need at least as many points as two points, so it means that if you assigned just two values ​​there for Okay and now see here when I put a value for here I have 1 and - 4 means 1 of the abscissa axis and - 4 of the ordinate axis and if you didn't watch the class in which I explained the Cartesian plane, go back and watch the class that has all the details for you too, right because guys, I say it again, it's very important in mathematics that you know concepts previous ones, you know, sometimes you fall here in this class and you don't understand what I'm talking about here because you missed attending the previous concepts classes, okay. And then speaking again here I have another ordered pair which is 3 of the value of Cartesian plane which is already ready here for you, see here the Cartesian plane are two axes that intersect, right, so they are perpendicular so I already placed it here at the meeting point at zero which is the origin, then I have one two three four then I put them all one by one, just to make it well organized for you, what I'm going to do now, folks, I'm going to take those points there, those ordered pairs and I'm going to form the point, so that means it's 1 on the abscissa axis, right? there the independent variable I will connect with - 4 of the ordinates which means the dependent variable here so it will be 1 I will connect with - 4 I formed my first point, ok?

Then the second pair is 2 and 0, but then when I have 2 and 0, it will be on top of this axis here, right, it will be on top of 2, so it will be right here, on top of 2 here, and the other is 3 of abscissa with 4 of the ordinates I will now connect 3 with 4 I am doing it without a ruler here people 3 with 4 see then that I have one two three points and with these three points I can already determine a straight line because when I make the graph from the AFIM function I have a straight line and then what are you going to do and then you are going to take your ruler and you are going to connect these points, oh, you take and connect these points so what am I going to do here now, connecting these points but I'm going to make a different straight line here, connecting a red straight line that I made here, it's better for you to visualize, look here at my straight line, is it straight guys, is my straight straight, oh there's a straight line that's not very straight, right? fix, there is a straight line that passed through these three points and what do I want you to observe now guys? Note that here on the X axis, where did it actually cross the Have you already attended another class where I explained the zero of a function, so go there and watch this class where I explained exactly about these zeros in the function, so mark it well, it crossed this point here at 2 on the X axis, it crossed at 2, and where will it be?

where would it cross our Y axis, which would be our ordinate axis that represents the value of the function, do you already have ideas? So let's go to the next one and I'll explain these two details to you, shall we? Guys, the other way I want you to learn to construct the graph of a function is like this, find for me where do I have the linear coefficient in the function, you forgot, look here, something like a function is f of X = AX + B o A is our angular coefficient o B the linear coefficient and if you compare this function here to this one you will see that B is the linear coefficient which is - 8 so it is the linear coefficient and this linear coefficient indicates where the our line will cross the ordinate axis so it will cross the ordinate axis at - 8 always like this Gis, always like this so here it will cut the ordinate axis at that value which is the value that does not have the letter with it is the value Is everything okay alone?

And how do I discover the other point, so I already know one thing, I already know that my straight line will pass here above this - 8 on the ordinate axis, which is the vertical axis, and how do I find where my straight line will go? pass here cross here the horizontal axis which is the axis of the abscissa which here represents the x you know it's easy you just need to find who the zero of the function is and how to make the zero of the function go back and watch Gis with all the details zero of the function so I need to calculate this the zero of the function and the zero of the function would be who it will be, right it will be so the function which is 4x - 8 for me to find I equate the zero of the function to zero because then I solve an equation, I took this function 4 x - 8 and equated it to zero. So let's go, 4 x will be equal to this 8, minus, plus 8 plus 0, which will be 8, then it will be x = 8 / 4 and 8 / 4 = 2, so guys, this 2 here that I found by doing the zero of the function, which is the zero of the function , which is the value of detail, it didn't pass point 2, even point 2 is marked here at that time, so it passes through point 2, which is zero here, this point here is indicating the zero of the function, but so that means with this just these two points and I can already make the straight line, that's right guys, because with at least two points I can build my straight line and that's it, just take your ruler and connect these two points, so that means I don't need to make that table, but not you, so you can look at yours function identify who the linear coefficient is and find the zero of the function then you find the two points where it crosses the ordinate axis and where it crosses the abscissa axis, vertical axis and horizontal axis ok so now just take and connect our our two points which are this one and here at - 8 and that's it I managed to do it.

So let's make my straight line here and see if it will work now, my straight line that it passed here at - 8, and remembering people that it is continuous , right? do it like this, then we made my straight line o my straight line more people o ruler take the ruler do it right people o take connect the point - 8 with point 2 o and draw your line. So see that here I have the straight line that represents the function 4x - 8.

Did you see how quickly you want to do it like this? Oh, so I hope that all the others can do it like this, do you want to do one more example just like this, which is practical, let's do one more example so then you can rock the activities, let's go? Quickly guys, this example here builds the graph of the function f of x = - 2x - 4 so what do you have to know where it cuts my line, right what will the graph be?

There it cuts the ordinate axis at what point I have to look at that value that is the linear coefficient, that value that is alone in the function, and that value that is alone in the function, look here, is - 4. So that means that it will cut the ordinate axis at - 4 or here o - 4 it will be at this point here that it will cut and for me to find out where it will cut the abscissa axis which is that point where it crosses the X axis I have to find the zero of the function zero of the function just take minus 2X - 4 which is the function and equal to zero that's all it solves, it will be - 2x = 4 positive because it goes there and changes the sign and then it will be x equal to 4 divided by - 2 which is - 2 so this value -2 It's indicating to me where it's going to cut the so the behavior of my line. And then let's do our straight line again with the ruler or with the gis ruler here, so it will cut the - 4 which is this point here and the - 2 which is this point here, oh this one is easy guys Call here, okay, you can make it more long, right?

You can go there and make it more long, your straight, there's no problem not doing it longer, and if you want to make it prettier, but you don't have to , right? ? Is production straight?

And then we managed to construct the line that determines then this function passed through the point - 2 which is the value here of the zero of the function and passed through the point - 4 which is the value that is alone here but you must be thinking that the - 2 here, because it's - 2 no, folks, that one there is the angular coefficient, okay, it's used for something else that I'll explain in the next classes, but it passed in - 2 here because it's the zero of the function, right, mark this well and you'll be great in activities. Don't forget to watch Gis' other classes on function so you know everything, take the opportunity to subscribe to the channel and leave a thumbs up and I'll see you in the next class, bye. .

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