 Hey everybody, welcome to Tutor Terrific. In this video I'm going to look again at the TI-83 plus graphic calculator We're going to do a video all about the analyses you can do with the graphing features on this calculator Now these are very very very close to the same features and the same buttons and commands that you would use for all the TI-84 calculators as well So this video can serve as a tutorial for those same features on that set of calculators So here I have the TI-83 plus and we are going to graph now If I turn the calculator on and you do some calculations It's not clear how to get to the graphing features on this calculator But in order to start a graph you need an equation to graph So here's what you do you press the y equals button here Now as you can see I have one plugged in Now what I can do with this in order to see the graph on a Cartesian coordinate plane is press graph Okay, and now if it hasn't graphed there before it's going to actually show this little blinking light here And it's going to actually graph from left to right But here's what that looks like you could see the origin of your Cartesian coordinate plane You could see the tick marks and you can see the axes and you can see the graph itself Now this is the default window for your graphs Okay, now let me explain what I mean if you press the window button here You could see with the min and max values for the x direction and the y direction are Here it's negative 10 and positive 10 for both min and maxes respectively and the increase So the tick mark values are equal to one Okay, if we go back to the graph you could see that there are ten tick marks in each of the four directions From the origin now this screen is not a perfect square So the the the actual aspect ratio is not one to one the x Direct the x-axis is a little bit more stretched out than the y-axis is okay Now let's say you wanted to adjust your window to see to see things differently Well, you could do that right from the window button Let's say I just wanted to see the first quadrant just positive x and y values What you would do is you'd make your x min zero and your y min zero You can do an overwrite feature like that and it'll override the entire previous setting And then you could press graph to see how your changes have affected your graph Now you can see that we're just looking at the origin in the bottom left corner and the tick marks to the left Excuse me to the right and upwards are all that are visible. So this is the positive quadrant of the graph Now we can go back if we want to reset our settings to be the original settings We could press a button called zoom for a lot of different shortcuts to window editing But one in particular that we like is zoom Standard we press six or enter when we're on it And this resets everything Back to the way it was in the standard window negative ten to ten in both directions. Okay What if we were graphing instead of a nice function like so we were we were graphing a trig function, okay? The trig function. Let's say would be sine X All right, I'm gonna erase everything else here the delete button We're gonna do sine X. Okay. If I were to graph that right now, it would look okay But it wouldn't necessarily take up a lot of the space on the window What can you do to adjust that so that it looks a little nicer for you? And also I want you to notice that the tick marks do not really line up 1 2 3 4 5 6 7 8 9 10 with the tick marks We'd like to graph and we use when we manually graph the trig functions We would like to see things like pi over 2 pi 3 pi over 2 and 2 pi Well, there's a zoom button feature just for that and it's called zoom trig. So press the number 7 If you look here, it's zoomed out on the y-axis I mean it's zoomed in on the y-axis and it's zoomed in on the x-axis But it's reset the tick mark so that they're every pi over 2 look at the window button to see these changes X min is now negative 2 pi basically and x max is approximately 2 pi and the the increase in the tick marks for x is 1.57 which is about pi over 2 And you could see the y-min and the y max we reset from negative 10 to 10 and are now negative 4 to 4 So this is what you want to use when you're graphing trig functions Okay, let's go back to y equals and let's graph a function that has some bad behavior in it. How about 1 over x Plus 2. Okay. Now, let's graph this guy in the normal viewing window So let's set zoom 6 And I'll go back to the normal window. Okay What you could see here is a graph that has an asymptote Now a lot of these asymptotes do not show up very clearly in the TI 83 They've really improved that with the color addition of the TI 84 and all that's different types But in the TI 83, there's a little bit of a glitch and you could see that it sort of skipped a pixel and gone over a little bit gone around the The tick mark where it should be at x equals negative 2 if we zoom in we can actually see That asymptote better. So if we go to zoom and press 2 and Press enter it will right now zoom in on the origin However, we can move the center of zoom around and right now you can see I'm moving it to the left And it's that little plus it's gonna center my zoom around there and the zooming magnification is around times 2 So I'm gonna put that right at the x equals negative 2 tick mark You can see the resolution Improves dramatically for your asymptote when you zoom in and that's good But I wish it was we obviously wish it was really nice at the start now That's what asymptotes look like and that's how you could zoom in now. Let's say you wanted to zoom out Zoom and then press 3 and again, you're gonna center your zoom out if you want to zoom back out around the origin You just move this back over To the origin make sure you see the tick marks and press enter it'll go back to the original Alright now, let's look at another type of graph that will allow us to calculate and analyze some things about a graph I'm gonna go back and I'm gonna get out of here. I'm gonna put in a nice graph. I'm gonna put in 2 x to the cube power minus 8 x squared plus 3 x oops a plus there over right that put it plus there plus six Let's see what this looks like Okay a nice graph that's gonna allow us to analyze quite a bit of things We can calculate so many things about these graphs But first I want to show you the trace button the trace button allows you to actually follow along Your graph and see how the x and y values of certain points Fluctuate as you move from right to left or from left to right So what you're adjusting are the x values with the left and right button You cannot go up or down on the graph with the up or down arrows that does not work And it's all based on x or y x x right or left values So the trace feature allows you to see Approximately the x and y values for certain points not every point there are resolution Drawbacks to this feature, but it is nice to be able to just look around and see the values But beyond that we want to do a lot more type of analysis and the way to do that is to press second trace Second trace gives us this calculation menu. We can calculate all sorts of things for example first Let's calculate a value What we're allowed to do with calculate value is we're allowed to plug in a certain x value Let's say two if we plug in two into here It'll calculate the y value for that x and it'll show me where it is Negative four specifically you could press another one by just pressing the value That you want and it'll reset that and you can find the new value 71 very very useful but let's say we wanted to calculate where certain things occur such as Zeros or where the x intercepts are that's another term for that press second trace To or move down to two and press enter Now we are calculating the x intercepts if you look at this graph There are three of them and so you have to tell the calculator which one you want to look at with the left and right bound feature So right now my cursor is moving around the graph left to right Let's say I want to find oops excuse me back to the graph second Calculate zero Now let's say I wanted to find this middle zero right here, okay? I'm gonna move like it says left bound I'm gonna move to the left side of that zero making sure that I have no other zeros Between the one I want and this cursor, okay? So this is on the left side of just that one zero and I press enter it puts an arrow up there, okay? Now explain what those arrows mean in a second now Let's move to the right bound which means we're gonna move to the right of that one zero making sure to not put any Other zeros in between us and that cursor, okay? Press enter again What these two arrows tell me is that it's gonna calculate a zero between those two values those two x values and It says guess it's not really guessing. It's really calculating it You press enter a third time to make it find it So the zero that particular zero occurs at x equals 1.401 Etc. Now the y value we'd expect at that point it to be zero Now the resolution Limitations of this calculator sometimes give you these glitches This is actually one times ten to the negative twelve in the calculators language that little e is a shorthand for that times ten to the exponent and That is essentially zero. It's one one trillionth. So it's really Approximately zero so that's how you calculate is zero. What if we wanted to calculate now some of these extreme Relative or local extremas we could do that Second calculate we would use buttons three and four. Let's do a minimum right now Now we could see a local minimum or a relative minimum down here. So we put our Cursor on the left side of that making sure there's no other extreme up between us and That minimum and we go to the right side of the minimum Make sure there's no other extrema don't go too far and now press enter a third time it's going to calculate the minimum value in that region in that interval and There's the x position of that minimum point and there's the y value for that minimum point So the relative minimum of this graph would be negative five point two five nine Approximately now. Let's do find out what this maximum is. It's really the same Procedure, but you just press the number four instead So we go back here We go to the left side of that maximum we move until we're just on the right side of that maximum and press enter twice and It calculates it for us it happens at point two oh two nine on the x-axis and the value is six point two nine six approximately Now there's one more thing I want to show you before we move on to multiple graphs And that is the table feature of our graphing utilities. So if we press second graph We get a table which shows us the values Of x that I previously plugged in for another problem to start with now Let me show you how to set up the table so that it looks pretty much normal Like you would used to be we could set where what x value we want the table to start at we could show Or determine how much each value is separated by in this case It'd be the integer one and then down here We can set the independent to either ask which allows us to pick values that we'd want To see the y values for or auto which will just start at zero and go up by ones So if we press second table now We could see that our x values are increasing by one starting at zero and we can't adjust What those x values are and this can be annoying for some people who want to analyze a particular section of a graph numerically what you would do in that case is you'd press second window and then make the independent variable ask Ask like that. Okay. Now what this does if you go back to second table Is it won't populate it with anything because it's waiting for you to ask it so five four three eight point one For example, so I'm plugging in the x values. I want to see this is very useful for people who are calculating Numerical limits for example, I want to get really close to tenth a hundredth in a thousandth away on either side Of a particular x value that might be undefined So that's how we use the table feature now. Let's look at What you could do when you have multiple graphs? So I'm going to put in on the y2. I'm going to put in another graph and you can put in as many as you want I'm going to put it a nice and easy point five x Minus one. Okay, so one half x minus one a linear function and when it goes back to the graph I now have two graphs showing The cool thing is that if you have graphs that are really similar in shape and you want to differentiate them You can if you go back to y equals and you go over here when you see the type of line here This slanted line what this represents is how the graph shows up. You press enter. You have multiple options You can have a thick line You can have a shaded region You can have a shaded region below You can have dots with little holes in them and you can have just little dots or you can have little dots like this Okay, so let's try this one when this is selected My first graph is now a collection of dots which are evenly separated Instead of a line now This is for the purpose that I want to show you today very Unusful to us. So let's go back and switch it to something else Let's switch it to and this is a cycle so it goes through this is it to a thicker line press graph Okay So if you had two similar polynomial curves you could differentiate which one is which with that feature Now what we're going to do is we're going to actually calculate Something with these two graphs now that the thing that being it's very useful for us with two graphs would be number five The intersect feature the intersect feature allows us to figure out where these graphs intersect now If you have multiple curves more than two I mean you would need to choose which two you are dealing with So for me, I only have two curves. So I just press first Curve and second curve But I want to put my cursor on each near the intersection. I want to calculate there are three intersections For this particular set of graphs and so I'll put my cursors near this leftmost one and press enter twice It's going to calculate that intersection and it happens at negative seven point three seven and negative one point three six So if you were to calculate this algebraically, that would be one of your three answers Now there's more answers because there's more intersections. So if we wanted to find another intersection Second calculate second trace five. We're going to move my cursor, which is now on the first curve Close to my next intersection and press enter it actually puts the cursor on the other line right next to it and Then you press enter twice and it will calculate that intersection which happens to be at one point four on The x-axis and negative point two eight on the y-axis Now what would the table look like when I have more than one function? well, if I press second table right now got my Previously asked for x values, but I have the y-values from the first equation and the y-values from the second equation I can go ahead and by the way change any of these overwrite with a new value Or I can go down to the bottom of the list and add more Like so and I can add as many as I want and see the y-values for both equations Alright, let's say instead of a graph You have data and you wanted to plot that data. Okay first. Let's get rid of all our graphs and let's go ahead and first Set our window to something that would be plottable like statistics data We'd get rid of the x and y negative values So the y and x means would both be zero then we go to stat and Press one for edit We have our data from our previous table actually from a Recent set and what I'm doing now is I'm editing L3 so that there's no data in it So I just have bivariate data One x value and one y value and here is my data right now I can actually plot that data by pressing second So we're once we're in this stat plot menu. We would pick plot one We're going to set plot one to plot the data we had in that stat edit window And so I'm going to turn plot one on to start and I'm going to make sure it's this original type which would be data in a simple graphing window not any of these other box and whisker plots or histograms or other Data like that. It's not the kind of data We have we just want to make sure that the x-list is L1 and the y-list is L2 now They're default to something else L purge 5 and L purge 6 So you want to set them to L1 and L2 by pressing second and you see for on top of number one You see L1 that sense for list one so make sure it says that and for why you'd set second to to make that list to now you have three different types of marks for your data points and pluses Squares or dots, so let's pick squares so it shows up easier now. We can quit this window It's going to save our settings. We go back to y equals and we see that plot one is now turned on We can of course turn that off by going up to it and pressing enter and pressing enter again Turns it back on with all of our settings and so now we can press graph and It shows our data points and we can graph this data with functions as well and it won't mess them up So if you have like a linear regression feature You're trying to graph your line with your regression your linear regression. You can do that This won't be a good one, of course, but you could show that you can graph lines and data points all together Okay guys, this has been a short basic tutorial on how to use the graphing features of your graphing calculator Stay tuned for more right now. This is Falconator signing out