![]() Going distance two there, and then five up, and then that's gonna give us some Here, we think of going one in the x direction, thisĪxis here is the x-axis, so we want to move distance one there, and we want to go two in the y direction, so we kinda think of Plug the triplet (1, 2, 5), and to do that in three-dimensions, we'll take a look over Things together, the natural way to do that is to think ofĪ triplet of some kind. So how do we visualize that? Well if we wanna pair these Think of as pair of points, we might have a pair of points like (1,2), and the output there is gonna be one squared plus two squared,Īnd that equals is five. This guy, but this case, inputs are something that we The relationship between inputs and outputs of Three-dimensional space at out disposal to do with what we will. The graph right now, let's just think we've got Of multi-variable functions, you know, not gonna show But this is kind of aĬonsequence of the fact where we just listingĪll of the pairs here. Output as being the height of the graph above each point. Think of as the input one, and this is the input two, and so on, and then you think of the Is that we typically think of what is on the x-axis asīeing where the inputs live, you know, this would be, we Might not draw this super well, is some kind of smooth curve. Possible input-output pair, what you end up getting, I You know, negative one, one, you go negative one, one. ![]() May kind of mark our graph, two here, one, two, three, four, so you wanna mark somewhere here (2,4), and that represents an input-output pair. Point, let's say we are gonna plot the point (2,4), so we With graphs is you think we just plotting theseĪctual pairs, right? So you're gonna plot the Pair is pretty incredible, the way we go about this Good intuitive feel for every possible input-output And the fact that we can do this, that we can get a pretty Understand all the possible input-output pairs. And here those are both just numbers, so you know you input a number like two, and it's gonna output four, you know you input negative X is equal to x squared, and anytime you visualizingĪ function, you trying to understand the relationship between the inputs and the outputs. So the two-dimensional graphs, they have some kind of function, you know, let's see you have f of Two-dimensional graphs and kinda remind ourselves how those work, what it is that we do,īecause, it's pretty much the same thing in three-dimensions, but it takes a little bit And before talkingĮxactly about this graph, I think it would be helpful, by analogy, we take a look at the So the one that I have pictured here is f of (x, y) equals x Three-dimensional graphsĪre a way that we represent certain kind of multi-variable function that kind of has two inputs, or rather a two-dimensional input, and then one-dimensional So what I'd like to do here is to describe how we think about
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