# Tagged Questions

Questions regarding the plotting or graphing of functions. Questions about graphs with vertices and edges should use the (graph-theory) tag instead.

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### How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new transformation....
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Let $f: (0,\infty) \to \mathbb{R}$ be some continuous function. We say that $f$ is subadditive if the bound \begin{align} f(x+y) \leq f(x) + f(y) \tag{1} \end{align} holds. I was attempting to ...
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### Why does this odd glitch exist with graphing programs?

In Grapher on Mac and the TI-84's built-in graphing program, there is a problem with imaginary numbers. If I input $i\sqrt {x}$, the graph ends up looking like this, even though it ought to look like ...
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### What would the graph of $y=\sin(\log x)$ look like?

What would the graph of $y=\sin(\log x)$ look like? So far I have dawn the conclusions : At $x=1$ $y=0$ The graph never touches $x=0$ ($y$ axis) The maximum is attained at $x = \exp(\pi/2)$
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### Is my graph correct?

My problem told me that: Let $S$ be the surface described by the equation in cylindrical coordinates $z = r^2$, and the inequality $0 ≤ z ≤ 4$, oriented such that the unit normal vector points ...
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### Fourier Series of the batman equation

I want to represent the batman equation as a Fourier Series. (I got the equation here : Is this Batman equation for real?) But a part of it is an ellipse and when I tried to calculate an the integral ...
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### Graphing the derivative from a graphed function

For the graphs of $f(x)$ make a sketch of the graph $f'(x)$ Here are the sketches I have so far. The graphs on the top row are the original functions. Did I graph these correctly?
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### Why is the graph of 4 nodes and 2 edges not self-complementary?

I am having some trouble seeing why a graph of 4 nodes and 2 edges is not self-complementary such that G is isomorphic to G bar (G complement) (please see the attachment below). I know that the number ...
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### Differential Equation Direction field

What i want to achieve: I want to plot the direction fields of the following three differential equations: 1. Malthusian growth model: $p'(t)=\lambda*p(t)$ with $\lambda=1$ and $p(t)=t$ 2. Linear ...
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### Is there a way to graphically show that a solution is the minimum or stationary solution to a functional?

I'm looking for the functional analogue to the visual representations of function optimization you most commonly see. To illustrate, if we have some function: $$f(x) = (x-1)^2+1$$ We can look at ...
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### What function has a 3D graph that will look like a spiral into a singularity?

I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint. I think a function that defines a black hole/singularity surface might look something ...
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### Math software for plotting phase portraits

I'm looking for math software which is possible to plot phase portraits for ODE and systems of differential equations. Is there a software which can create not only simple 2D phase portrait plots but ...
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### Plot histogram and density function

I need to plot a histogram for the data: ...
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### $x^{y}=y^{x}$ Intersection Question

I'm looking at this problem, $x^{y}=y^{x}$ and the question is to find the point of intersection of the two curves that form a solution set. I understand how to find the point of intersection using a ...
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### Creating a function from graph

I'm trying to create a function that will generate a graph similar to this awesome paint gif: This is my attempt thus far: f(x)=-0.0040*(x+200)*(x-200) I can't figure out how to get my graph to "...
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### Should a “good” equation divide the plane?

At the question Is there any equation for triangle? (MSE) the answer given by Henning Makholm received the most upvotes. Therefore let's define the following triangle function $H$ with (a,b,c) the ...
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### Using Graphs Changes the Solutions for Diophantine Equation? Imperfection of Graph?

Solve the Diophantine equation $$x^2+4y^2=z^2$$ The problem here is that I derived solutions using two different methods, and the both solutions do satisfy the given equation yet they are not ...
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### how to choose point spacing to approximate a parametric curve using line segments?

Suppose I have a parametric equation for a curve $\vec{r} = f(t)$, which I wish to draw using line segments between some set of points at times $t_0, t_1, t_2,$ etc. If I want to achieve a given ...
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### Find a function (curve fitting) for given values

I am trying to assign scores for URLs based on their view counts. I have about 300,000 URLs. In a two-day interval, only 1 URL got more than 5000 views 8 got between 1,000 and 5,000 views about 500 ...
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I am writing a library for graphical LCDs and I want to incorporate a function to draw a circle on the screen. I have already succeeded in drawing simple circles, however, I want to be able to pass a ...
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### planarity of graph as a consequence of its flow

Is it possible to distinguish planar and non-planar graphs (networks as a matter of fact) by flows? That is, is there a flow criterion for a graph being planar or not?
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### Iterating a relation to find a function

I was playing around with a graphing calculator, trying to find approximations for inverses of $f(x)=x^5+x+1$. This cannot be expressed with radicals or the like, but I wanted to see how close I could ...
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### How to graph 3D functions of two variables on Wolfram Alpha?

How to graph this on wolfram, google, or other free software: \begin{alignat*}{3} x(s, t) &= a\cos(mt) \cos^{k}(ns) &&\cos(t) &&\cos(s), \\ y(s, t) &= a\cos(mt) \cos^{k}(ns) &...
If we have a two functions $f:[-1/2, 2] \to \mathbb{R}$ $g: [-1/2,2] \to \mathbb{R}$ $f(x) = [x^2-3]$ where $[ \cdot ]$ denotes greatest integer $g(x) = |x| f(x) + |4x-7| f(x)$ Now we have to ...