Solving equations graphically (2 of 2)

in the last video we estimated the solution to e to the X is equal to 1 over X times X minus 1 times X minus 2 using a calculator we got a first rough estimate by just looking at this graph and then we tried values out it's really zero in on or get close to the x value where this is true what I now want to do is actually just use the graphic the graphing functionality of this calculator to try to estimate the solution graphically so let's go to graph and what I'm going to try to do is graph both of these functions so the first function let me clear this the first one is e of X which in this on the graphing calculator will be y1 and that's going to be e to the X power and then the second one the second one y2 will be R of X which is going to be 1 divided by x times X minus 1 X minus 1 x times X minus 2 X minus 2 and so let's you have to close this parentheses as well so I've entered in the graph and I also want to I care about where we zoom in so I immediately want to zoom into this part of the graph right over here so let me go to the range so actually there's also a zoom functionality that I could use but let's let's actually let me let me do that that that could be fun so let's let's just let's just graph it actually let's just see what range it's graphed at right now let's see what we would care about let's start with kind of a rough approximation just to see that this is indeed the same graph so let's start with X going from 0 up to I don't know two three so this would be this part of the graph right over here and then the X scale is one that's what they'll mark off every one we could even mark off every 0.5 if we want like this one is marked off every 0.5 and the Y minimum let's go from 0 to on this range actually goes pretty high and the way this is graphed goes all the way up to looks like 10 so I'll go to 10 I'll leave the y-scale as one they mark it off every one right over here and now let's graph this thing and that was a of X and now it's graphing R of X and you see it indeed looks pretty similar to what we have here now what we care about is this point or on our calculator this point right over here we want to figure out what x value what is the x-coordinate of this point of intersection this is when our two functions are equal to each other so let me zoom in on this so let me I think I could use this box luck functionality so it essentially lets me construct a box around this and it's going to zoom into that box so I'm going to get is tight in on this as I can go so if I press I can get even tighter on it so if I press ENTER now I can define the other corner of the box so that's pretty good I'm going to zoom in press ENTER and now it's zoomed in on to that little teeny box so that was a of X and now it's going to graph R of X so now let me try to trace the graph so I don't see trace so it's letting me Tracie of X and let's see if I look at my x values decrease so at this point a of X is still higher than R of X and if we get right over here so two point zero five six we see that R of X is above we see that R of X is above a of X we just see that graphically and then we're left we're left of the point of intersection and then we're still left of the point of intersection now we're right of the point of intersection so it looks like the point of intersection is between two point zero five seven and two point zero five nine and so in the previous video when we said it was well where our estimate was two point zero six we were definitely within one we were definitely within 0.01 of the point of intersection if we did want to get even more precise we could we could zoom in more and I encourage you if you've got a graphing calculator like this to to actually try that out