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

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282 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
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172 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
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54 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
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0answers
20 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 ...
2
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43 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: $$ ...
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52 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 ...
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60 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 ...
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58 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 ...
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75 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
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190 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 ...
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118 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
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76 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?
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160 views

My solution is right and the book is wrong (parabolas) or did I misunderstand it?

Find the equation of the parabola with the vertex at the origin; directrix 2x = 3 So what I did is, find the equation of the directrix $$x = \frac{3}{2}$$ and then because its the directrix, the ...
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200 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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21 views

Graphing a complicated equation

How do I draw the graph of this equation $p(\theta^{*} (x))\hat{G} - (1-p(\theta^{*} (x)))(\bar{P} - r(x)) = \check{G}$ Here the $\check{G}$ is a positive constant and is a straight line, but how ...
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20 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 ...
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25 views

Circular node, direction of trajectories?

I have a problem that is a circular node: $\begin{bmatrix}0 & 1 \\ -1 & 0 \end{bmatrix}$ gives $\lambda = \pm1$ It is complex on both, so it is a circular node. Using equilibrium points, we ...
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16 views

Given a function and its transformed graph, find an equation of the transformation

Given a parent function and its transformed graph, I need to find an equation of the transformation. I cant seem to figure #13 or #14... I get confused with which points to start with when dealing ...
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35 views

Drawing Phase planes with one input, rather than long scripting

What software can be used to draw phase planes easily? I want to input some $\begin{pmatrix}x_1 \\ x_2\end{pmatrix}=$blahblah, and have it plotted with or without initial conditions. Is there any ...
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28 views

Help with understanding how to sketch a graph of y=1/f(x) and y = xf(x)

I'm having problems trying to figure out how to sketch a graph for these 2 questions. Could someone provide me a step by step guide on how to do this? Thanks in advance.
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31 views

A rectification, what is the graph of the following?

What is the graph of y=y(x) of: $\sqrt {{{(x - 2)}^2} + {y^2}} + \sqrt {{{(x + 2)}^2} + {y^2}} + \sqrt {{x^2} + {{(y + 2)}^2}} = 16$ Thank very much
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48 views

What kind of trend, and relationship is this graph?

I need some help with labeling the trend of this graph, and also deciding what the relationship is between the two variables (X,Y). Here is a picture of it: The Excel document can be downloaded ...
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46 views

Representing distances in high-dimensional space

I have a set of n points $P_i$ $(i=1..n)$ in an d-dimensional space. I can calculate the distances of every point to each other point. What is the best way to represent the distances of these ...
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20 views

Is there any interactive spline fitting software?

I'd like to know if there's any software (freeware) for interactive data interpolation. What I want is to be able to visualize my data on an XY plot and drag the points to see how it affects the ...
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45 views

Graph of f(x) = the first number in the decimal expansion of x

I'm a bit confused about the answer given in the textbook. I take the definition of 'the first number in the decimal expansion of $x$' to mean simply the first number in its base $10$ ...
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93 views

Is there a name to this equation: $(y - a|x|^b)^2 + (cx)^2 = d$?

While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form: $$(y - a|x|^b)^2 + (cx)^2 = d $$ Where   ...
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87 views

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points?

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points? I don't quite the understand the solution which is in ...
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139 views

How to plot decimals on a line graph?

Trying to plot 56.8, 113.6, 170.4, 227.2 and 284 on the x axis of a line graph, what scale should I use? And should it start at 0?
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41 views

Quartic Polynomial Manipulation

I have a quartic polynomial in $x$ (too long to write here) $f(x,c_1, c_2, c_2)$ where $c_1, c_2, c_3$ are constants which I have complete freedom over how to fix their values, as long as they are ...
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31 views

Plot histogram and density function

I need to plot a histogram for the data: ...
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42 views

What is the number of x-intercepts in this graph of sine?

The function : $y=3-4\sin(2\pi x-3\pi)$ .. how many $x$-intercepts over the interval $[0,2]$? I am confused if they're 3 or 5 because there are 3 $x$-intercepts that are really intercepting ...
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15 views

Shape of graph and plot

Suppose $x \in [0, \infty)$ and $y \in [-1,1]$. When we plot $y$ vs. $x$, we get an upward parabola shape. Suppose we plot $y^2$ vs. $x$. Would the shape also be approximately an upward parabola?
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61 views

How to find change points in a graph on matlab

I have a graph like this I need to find points at which sudden changes happening for the DPC Time Curve. We can observe that at time 20 and around 70 increase is happening. How to do this in Matlab. ...
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42 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 ...
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82 views

Physical shapes you can't simulate using mathematical functions

This question borders philosophy, so I would be happy to move it somewhere else if this forum is inappropriate. While doing some 3D function plotting, it occurred to me that I can plot any shape ...
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0answers
16 views

Weighting values using curves

I am in the field of computer programming but I think my question is maths based. I have tried several google searches on this matter but nothing has come up with what I am looking for, probably ...
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0answers
42 views

How does sin & cos affect audio waves

Given a function such as "cos (x) + 4 sin (3x) + 5 cos (3x)" when graphing it to produce a wave, are there any set rules to how you can adjust the function to produce a higher frequency, or increased ...
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23 views

Online tools for plotting and deriving formulas from set of data?

I have a matrix of 20x3 decimal values. I would like to have them in a graph, with one plot for each of the three y values. I would also like approximated formulas for each of the three. Are there any ...
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0answers
48 views

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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39 views

Visualizing a complex curve

This may be as much a question about computers as about math. Let $C=\{f(r,s,t)=0\}$ be a curve in $\mathbb{CP}^2.$ By forgetting about the points at infinity we can view $C$ as a surface in ...
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0answers
74 views

How does a piecewise step function work?

The wiki pages aren't helping at all. What is a step function and how does it work? I've seen them used in the floor, ceil, frac and even signum functions. And although it is easy to understand what ...
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0answers
14 views

How an I create a model population?

I need to crate a model population for my Math fair and this is what I have. I need some help with it -I want to find out the size of a population by using a natural exponential function -When I ...
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0answers
71 views

“Strange” plot of a difference equation

In this book about intertemporal optimization (page 33) I've found this difference equation: $x_{t+1}=ax_t \quad, \quad a>0$ The solution is: $x_t=a^t x_0$ where $x_0$ is the initial value of ...
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55 views

Given only the graphical representation of a curve, how can I find the function?

I'm developing an application which will: A. identify curves in 2D images using the generalized Hough Transform B. determine from the graphical curve the mathematical function needed to generate it ...
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261 views

How to plot a stream function

This question relates to fluid mechanics and I have the components in polar coordinates. The components of the velocity field are; $$v_r= \frac{-kr}{z}$$ $$v_z= kz$$ $$v_\theta= 0$$ and I have ...
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104 views

Splitting parametric curve equation into two ranges

I am examining the speed of motion on curves and in the textbook i am reading , the example was showing that using a parametric equation for an ellipse will result in a regular motion (as expected) , ...
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0answers
68 views

Graphing cumulative elevation gain along a route

I'm trying to develop a formula that will allow for a graph of the cumulative slope elevation gain along a route to be created. Currently I am using the Max value of the elevation along the route ...
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709 views

Graphically solving a Linear Programming Problem?

I was given the following linear programming problem and have been asked to find all optimal solutions graphically. I am quite new to the subject, so please forgive my naivety. ...
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229 views

Help to understand the concept of diminishing returns

Suppose I have this function: $q=f(k,l)=600k^2l^2-k^3l^3$ Then, $f_l=1200k^2l-3k^3l^2$ $f_k=1200kl^2-3k^2l^3$ $f_{ll}=1200k^2-6k^3l$ $f_{kk}=1200l^2-6kl^3$ $f_{kl}=f_{lk}=2400kl-9k^2l^2$ Now, ...
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61 views

How to calculate straight line into graph having variety of different results

How to calculate straight line into graph having variety of different results. What I mean for example let say we have this kind of results (measuring persons weight ...