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Consider the graph of the functions y = xand y = x(z? 4)....

Question

Consider the graph of the functions y = xand y = x(z? 4).

Consider the graph of the functions y = xand y = x(z? 4).



Answers

Graph the given functions. $$y=4-3 x$$

So for this problem we have the function Y equals two X minus four. And before we graph this um we are going to be plugging in different points of X. And getting the corresponding points of why? So plugging in say negative too gives us two times negative two. Which is negative, four minus four is negative eight. Then plugging in say a negative one, we end up getting negative one times two is negative two minus four is negative six. Then plugging in zero. We get ready to four. Okay, plugging in one. We get negative too. I'm plugging in two. You get zero. Yeah. Notice what happens when plugging all these points. What we've done is we've created a line and the line is a bunch of different individual points. Um And we could connect all these points using um a ruler and a pencil or just a pencil and carefully drawing the line. And what we end up seeing is that this is the same thing as if we connect all the points with this line right here. So we could use a graphing calculator to graph every single point. Um Or we could plot them individually and just connect the points to produce our line.

Mhm. So for this function here, we're gonna be graphing Y equals for over exposed to this is our graph right here, we know that the graph is going to be undefined it negative too. So we can look at it at a negative three. And that would give us a negative for Then at -4. We get a negative too. Mhm. And a negative five for negative six. Okay, we get a negative form, we see those points and then we can also do other points, such as um negative one. Give us four negative. Uh We have a positive two x equals two. Give us one. So by doing this we see all these different points of the graph, but ultimately they'll match up with our function, which is why you should always use a graphing calculator.

So we're gonna be drafting the function for over X squared. We see when we have this, this is gonna be Y equals forever expert. So when we plug in values for X will get corresponding values for why? So we can't plug in zero obviously, but if you plug in one Or -1 will get four. Okay? If we plug in uh two or negative two we'll get one. Mhm. And then if we plug in um for or negative for forget. Of course. Right. What you see is that these points are perfectly matching the graph. Which do I helpful to use a graphing calculator to verify your final graph once you've connected the points.

Here. This problem. We need to solve it for a while first to get a good, accurate graph. But I guess if you want to use a graphing calculator so it's gonna be X to the 2/3 minus four. However, because it had the Y plus four, we know that this is gonna be shifted down for anyway. So extra to third shifted down. Four is gonna be partially beneath the X axis. And so our Vertex is gonna just get moved down for so normally it would be at 00 I'm gonna go up 1/1 and then up for over eight, and then that'll get us the points where it crosses the X axis. Okay, thank you very much.


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