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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5
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115 views

Graphs of interesting integrals of the form: $\int \sin^a(x^a)\cos^a(x^a)$

Here are a few graphs of the form:- $$\int \sin^a(x^a)\cos^a(x^a)dx$$ Where $a$ is an even, positive integer. $a = 2$ $a = 4$ $a = 6$ Now, a few graphs of the form:- $$\int ...
4
votes
0answers
137 views

How do you call functions that fulfill $f(x)=\pm f(\pm 1/x)$?

A function $f(x)$ that fulfills $f(x)=\pm f(-x)$ is called (a)symmetric even/odd. How do you call functions that fulfill $f(x)=\color{blue}\pm f(\color{red}\pm 1/x)$? ...
3
votes
0answers
21 views

How does emergent oscillation appear in this animation of concentric circles?

I made this animation and I barely understand it. http://bl.ocks.org/tophtucker/500d2a010105cfcc87db It's a bunch of concentric circles with exclusion compositing. The radius of the ...
3
votes
0answers
44 views

Plotting a 4D Dynamical System

Suppose I have a 4D dynamical system. Each axis has a fixed point, and there are orbits connecting the fixed points. It looks something like this: Each $Q_i$ is a fixed point on each axis of a ...
3
votes
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142 views

Visualising surface integrals

For a current problem I am working on, I have run into angular surface integrals, i.e. the differential solid angle $\text{d}\Omega$. Specifically the surface integrals are defined by ...
3
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0answers
85 views

Plot implicit equation in sub-quadratic time complexity

It is fairly straightforward to plot an explicit equation such as $y=x^3+3x^2+2x+5$ in linear time, because you can just iterate through all $x$ in your graphing space and use the equation to ...
3
votes
0answers
108 views

Properties and representations of the the rescaled complementary error function $\mathrm{erfcx}{z}$

Consider the rescaled complementary error function: $$ \mathrm{erfcx}(z) = {e^{z^2}} \left( {1-\mathrm{erf}(z)} \right) $$ $z \in \Bbb{C}$ which also has the following integral representation: $$ ...
3
votes
0answers
71 views

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 ...
3
votes
0answers
445 views

Recognizing subadditivity

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 ...
3
votes
0answers
208 views

Sketching the graph of a function

How would I sketch the graph of the following function. Sketch the graph of a function satisfying the following conditions $f(1)=2$ $f(-1)=f(3)=-1$ $f'(1)=0$ $f'(x)>0$ for all $x<1$ ...
2
votes
0answers
26 views

Graphing/visualizing a complex parametric plot without using mathematica

I am trying to visualize the parametric plot in $\mathbb{C}$ of the curve $\gamma$ defined for $t\in[-\infty,\infty]$ as $$\gamma(t)=\exp\left(-t^{2}+\frac{t}{\sqrt{1+t^2}}i\right).$$ I think I find ...
2
votes
0answers
15 views

Plot complex inequalities $|z^2| > Im(z)^2$

I need to draw the set of all complex numbers, which satisfy the following inequality: $|z^2| > Im(z)^2$ This is what I've already done: $|z^2| > Im(z)^2$ $|z|^2 > Im(z)^2$ - use $z = a ...
2
votes
0answers
40 views

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 ...
2
votes
0answers
105 views

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 $x = \exp(\pi/2)$
2
votes
0answers
32 views

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 ...
2
votes
0answers
91 views

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 ...
2
votes
0answers
57 views

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?
2
votes
0answers
77 views

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 ...
2
votes
0answers
352 views

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 ...
2
votes
0answers
76 views

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 ...
2
votes
0answers
113 views

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 ...
2
votes
0answers
251 views

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 ...
2
votes
0answers
49 views

Plot histogram and density function

I need to plot a histogram for the data: ...
2
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0answers
56 views

$x^{y}=y^{x}$ 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 ...
2
votes
0answers
78 views

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 ...
2
votes
0answers
116 views

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 ...
2
votes
0answers
188 views

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 ...
2
votes
0answers
345 views

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 ...
2
votes
0answers
229 views

Ellipse radius interpolation with different radiuses

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 ...
2
votes
0answers
79 views

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?
2
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0answers
292 views

how to obtain state space diagram and state space model for transfer function

How do we obtain the state space diagram and state space model for transfer function for example the question is given How to draw state variable diagram for the given transfer function ...
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0answers
26 views

Discontinous and differentiable

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 ...
1
vote
0answers
21 views

forbidden chromatic polynomial

We wish to show below chromatic polynomial are not exist; It means that we couldn't find any graph that has one of these chromatic polynomial 1- $\ k^5 - 4k^4 + 8k^3 - 4k^2 +k$ 2- $\ k^4 - 3k^3 + ...
1
vote
0answers
7 views

Let G be bipartite on n vertices

Let G be bipartite on n vertices .Prove that $\alpha=\frac{n}{2} $ if and only if G has perfect matching.. Suppose $X\subseteq A$ and $|X|\gt n/2$ Then every vertex in B must be adjacent to a vertex ...
1
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0answers
17 views

Geometric interpretation of the nth root of a quaternion?

For ordinary imaginary numbers, $(r,\theta)$ turns into $(\sqrt{r}, \theta /2)$ for the square root and it is similar for higher roots. Is there an analogous interpretation for roots of a quaternion? ...
1
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0answers
33 views

Graph of a higher-order function

When we deal with functions which work on numbers, we can graph them easily: Just take each of its possible input values and find its corresponding point on one axis, then go straight up in its ...
1
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0answers
15 views

What are the expected number of people aged over 60 based on the following cumulative frequency table?

So, Question is as follows; It is expected that people who have reached the age of 60 will be drawing a state pension. If the countries poulation is 42.5 Million, what is the number of people that ...
1
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0answers
17 views

finding the equation of a graph with 2 given characteristics

I need to find the equation for the graph of $y = x^2$ with the following characteristics 1. congruent to $4x^2 + 8$ 2. shares the same translations as $\frac{1}{3x - 9}$ I have attempted this ...
1
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0answers
25 views

Why is it useful to find the domain and range of a function graph

I know about domain and range but my professor has asked us why it may be useful to find the domain and range and I cant really think of a reason that would be considered "useful". Can anyone think of ...
1
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0answers
20 views

Giving the equation for graphs of fractional powers

In Mathematics Methods we are learning the features of graphs of fractional powers. The equations of these graphs are in the form: $y=a\sqrt{x-b}+c $ By simply analysing a graph with a hyperbola how ...
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0answers
32 views

Symmetry in graphs of polynomials

I am learning graph skectching. Its well known that quadratic polynomials over reals are symmetric about their minima/maxima. But today I discovered an interesting result that Cubic polynomials are ...
1
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0answers
18 views

Determining function of Graph

Looking through some notes on numerical computation I came across the following graph: I know this is a longshot, but I'm not incredibly mathsy and would like to know what kind of a function this ...
1
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0answers
46 views

How can I plot the complex function in 2D?

My function: $$sin(wt-jT) \tag{1}$$ where $j$ - complex unit, $T=0.1,\ w=8 \pi,\ t=[0,0.01,0.02..100]$ I transform it to function with real arguments: $$\sin(wt)\cosh(T)+j\cos(wt)\sinh(T) ...
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0answers
20 views

From current plot $y=f(x)$ get plot $dx/dy$ vs $y$

I have a plot $y = f(x)$ where $y$ is voltage and $x$ is capacity. Now I want get from this graph the $dx/dy$ vs $y$ plot. How can I get this new graph?
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0answers
36 views

rotation of spherical surface in spherical coordinates

I need to plot a spherical surface in computer (like the surface of a lens). I know the normal vector (as an example, say $\ n=(1,2,3) $) of this surface and it originates from the centre of the ...
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0answers
72 views

How to Trace a Real-Life Flower Using Polar Equations?

Here is the flower I'm trying to trace: $\hskip2cm$ How can I trace this flower using polar equations? I currently have the formulas \begin{align} r_{1}&=1.75\sin(10\,\theta + 18) +3\\ ...
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0answers
37 views

Why use ln-ln plot in proportional hazard test?

I recently study survival analysis since couple of months ago, and there is one question which makes me curious. a simple and (maybe) a stupid question. Why do we prefer to use ln-ln survival curve ...
1
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0answers
36 views

Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.

Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.Here $\text{frac}(x)$ is a fractional part function. ...
1
vote
0answers
18 views

Picturing/Graphing (quasi-)concave/convex functions?

I understand the definitions, and can do work with them, but when I try to picture them I get confused (picture simple concave/convex functions that is, not some very complex ones obviously). ...
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0answers
24 views

Analytic formula for parameterizing the below family of curves

I'm trying to find an analytic formula for a curve that can look like any of the curves below depending on one or more parameters. My initial thought was to use exponentials, something that might ...