00:01
So we have this, well, you have a graph here, and we have two functions here.
00:09
Okay? and so in this question, we are to match the lines that represents the graph.
00:18
So we're the functions that we can see here.
00:21
And so we have to match, again, we're to match these functions here.
00:24
Y equals to this, y equals it is, y equals it, why to match those functions with the appropriate graph.
00:31
Or all line.
00:34
Okay, so let's start here, and one of the things that we could do here is to remember quickly the linear equation form, or the linear function form, which is y equals to m times x plus b.
00:51
In this case here, i see, in the case of f of x, okay? i do see that i have 8x plus 1.
01:04
That means that i perhaps i should write this in blue, instead i want to highlight things in red.
01:11
So my function f of x is x plus 1.
01:19
And so that means that this is my slope.
01:21
My slope is going to be, for this function, my slope is going to be equal to 1.
01:27
Because this is x times 1, right? times 1, essentially, right? there's an invisible 1 there.
01:35
And this is going to be my b.
01:37
My b here is going to be equal to 1.
01:40
So i'm going to look in the graph and see where first do i have an intersection of 1 with the y axis? well, i'm seeing that here.
01:52
Here, my b is 1.
01:55
Okay, this is my b.
01:57
And so that means, and then this graph looks like it is, it is going, so this is a positive slope, so i'm expecting something positive this way, right? and since it is, so this is going to be, for example, y equals to x, right? but since it's essentially raised up one, okay, it's raised up one is the way it's going to have the intersector form.
02:24
So my best guess right now is that this is going to be my slope.
02:31
This one here, the green one here.
02:34
Okay? so this is my guess.
02:36
My guess is that this is y equals to m times x, not m plus b, but y, this is my half of x.
02:45
That's my guess.
02:46
So the green one corresponds to, i'm going to move this one just a little bit ahead, because we're going to do something cool here.
02:54
So i'm going to guess that this is my...
03:00
This line here corresponds to my function ffx equals to x plus 1.
03:12
Okay, now there's a second reason why i believe that that's the case, because i'm going to show you something here.
03:18
Let's go to gfx.
03:20
Let's see what gfx has to offer us.
03:23
Well, g of x is going to be, well, 2x minus 1.
03:32
Okay? so 2x minus 1.
03:35
Well, first of all, i can see that my b is going to be negative 1.
03:43
Right, my b is negative 1.
03:44
I also have my slope here as 2.
03:50
Okay.
03:51
Now, this is the second reason why i'm confident, or i feel, okay that this is the graph of my f of x okay this is the second reason right now slopes i'm going to start if from your slope being undefined to a slope being your m being so undefined or vertical and to your m being equal to zero or you can say horizontal and there is this sweet spot where your m is equal to 1 and this is your diagonal that's at least how i call it that's a diagonal for m equals to 1 right if you were taking angles it's going to be at 45 degrees or pi over 4.
04:48
So as x rises y rises okay same pace but for anything here this region here this region here is the region that you could say m is between 0 and 1.
05:06
So m is fractional.
05:09
Now, by the way, this is for positive slopes.
05:11
This is for positive slopes.
05:13
For the negative side, you also have something like this for the negative side.
05:16
The same thing, just a few things are reversed.
05:20
Now, this is 0 is less than equal to m is less than equal to 1...