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

learn more… | top users | synonyms (2)

4
votes
0answers
113 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
19 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
0answers
137 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
votes
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
70 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
444 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
205 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
38 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
88 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
88 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
334 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
75 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
242 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
48 views

Plot histogram and density function

I need to plot a histogram for the data: ...
2
votes
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
115 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
185 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
344 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
votes
0answers
289 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 ...
1
vote
0answers
29 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
vote
0answers
31 views

Find the number of points of distance n away from origin as function of n

I came across a seemingly simple problem the other day and I thought I'd share it with anyone interested. Say you have a point in 3 dimensions. The number of points that are of distance $0$ away is ...
1
vote
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
vote
0answers
29 views

Model linearly: Determine amount of units for production

A company produces 2 products in a week. Let $x_i$ denote the number of units of product $i$ to produce. Each product requires liters of Chemical X to make. Info is given below: \begin{array}{|c|c|} ...
1
vote
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
vote
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
vote
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 ...
1
vote
0answers
31 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
vote
0answers
17 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
vote
0answers
45 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) ...
1
vote
0answers
19 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?
1
vote
0answers
34 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 ...
1
vote
0answers
65 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\\ ...
1
vote
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
vote
0answers
35 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
17 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). ...
1
vote
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 ...
1
vote
0answers
31 views

What kind of topological sorting exists in graph theory and what are their graphic plotting?

I know that there is at least two kinds of topological sorting: "by rank" and by"level" a level of a vertex is the maximal length of a path with x as an extremity. a rank of a vertex is the maximal ...
1
vote
0answers
13 views

Number of hyperbolae from 3 points with a known absolute difference in distance

In GPS, measuring the correct distance to satellites is not possible due to clock errors in the receiver (what you measure is called a psuedo range because it is based on incorrect time which ...
1
vote
0answers
43 views

Parametrization of helicoid like surface for Faraday's law of induction of a solenoid?

I want to visualize with mayavi a possible surface for Faraday's law of induction in the electrodynamics of a solenoid. I.e. something like a helicoid with a smooth transition to a rectangular area, ...