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Depending on your point of view, you may think that Tupper's self-referential formula is trivial, or totally awesome. ;) Though it's not funny, but one of very beautiful graphs is "The Love Graph". x = 16sin3 t y = 13 cos t − 5 cos 2t − 2 cos 3t − cos 4t x = 16 sin 3 t y = 13 cos t − 5 cos 2 t − 2 cos 3 t − cos 4 t.
In which order do I graph transformations of functions? The 6 function transformations are: Vertical Shifts. Horizontal Shifts. Reflection about the x-axis; Reflection about the y-axis; Vertical shifting or stretching; Horizontal shifting or stretching
There are a lot of different tools to graph online, by example I discovered today the library plotly that can be used in many programming languages (and online too!). It homepage is full of tutorials for any kind of plot, in our case we have a tutorial for a curve in $\Bbb R^3$ here.
0. The graph (1) G of the function f: X → Y is the set {(x, f(x)): x ∈ X}. Unless I'm mistaken, this can be interpreted as a directed, bipartite graph (2) where every vertex in one of the partitions (domain) has out-degree 1 and in-degree 0. The other partition is the image. CLARIFICATION: graph (2) refers to the graph-theoretic definition ...
You could also write down the procedure for generating the Koch snowflake or the dragon curve as an equation. (Formally, the former is called "snowflaking a metric", but the notation and concepts are probably a bit above your audience.) These also help make the point that, from one perspective, functions are procedural.
A perfectly correct answer that was posted below (and accepted) tells us how to rotate the graph of any equation relating x x and y, y, even if the equation cannot be written in the form y = f(x). y = f (x). For example, you can rotate the graph of y2 = 4 − 2x2, y 2 = 4 − 2 x 2, which is an ellipse, by this same method. – David K.
Now, I'm looking for means to graph any non-functions, not just simple ones such as a circle or a sideways parabola, which simply require the graphs of +f (x) and -f (x). Maybe more complicated ones such as sin(x) + sin(y)= 1. The following graph is of the said non-function, as graphed by Desmos. Any help on how to graph non-functions is ...
$\begingroup$ as others said first you have to find the parts in which both functions exist which is [-4,3] and then you have to add the values of each function and put the new point on the graph. for g(0) and f(0) it is (0-2)=-2 and also you have to do this for each point and graph whole function of h(x)=f(x)+g(x) $\endgroup$ –
0. Since h(x) = (f + g)(x):= f(x) + g(x) h (x) = (f + g) (x):= f (x) + g (x) for every x x in the domain, the graph is the one that you obtain summing the two functions pointwise. That is, at x =x0 x = x 0 will correspond the point h(x0) = f(x0) + g(x0) h (x 0) = f (x 0) + g (x 0). Edited after seeing the comment about discontinuities: if one ...
A function is not the same as its graph, nor is it the same as its level curves. I think it gets even worse for my poor Calc III students, who have to integrate functions of three variables over three-dimensional solids. There it is hopeless to think of graphs, because the graph of a function of three variables lies in four-dimensional hyperspace!