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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392
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10answers
404k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
3
votes
2answers
2k views

Using equations to draw out complex objects

How do people come up with equations of curves to draw out complex objects? Some popular examples would include: batman curve & PSY curve. This stackexchange link explains the rationale for the ...
7
votes
3answers
25k views

Is there a way to rotate the graph of a function?

Assuming I have the graph of a function $f(x)$ is there function $f_1(f(x))$ that will give me a rotated version of the graph of that function? For example if I plot $\sin(x)$ I will get a sine wave ...
4
votes
1answer
262 views

Can the graph of $x^x$ have a real-valued plot below zero?

The function $f(x) = x^x$ gives a complex number only if x has an even denominator. I'm not sure about irrational numbers. Why, then, is the best graph I can find of that function that of Wolfram ...
2
votes
3answers
340 views

function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?

Let $f(x)=x^{-(1/3)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from -1 to 1. Which of the following statements is/are TRUE? f is continuous in [-1, 1] f is ...
3
votes
3answers
1k views

Define a graph with segments or boundaries

This question is quite simple relative to the normal content on this site. (and please rename the title as I don't know what the proper definition is) Is it possible to have a function such as: $y = ...
8
votes
5answers
15k views

Is there any equation for triangle?

Like there's an equation of a circle, is there any equation of a triangle? I've been trying to build one and the closest thing I've managed to do is to create an equation of 2 lines and use the $x$ ...
8
votes
2answers
24k views

Piecewise function plot in Matlab

Is it possible in Matlab to plot an even piecewise function like: $ f(x) = \begin{cases} 3t , 0 < t < \pi \\ -3t , -\pi \le t \le 0 \end{cases}$ which has a period of $2\pi$. I ...
7
votes
4answers
7k views

What is a good graphing software?

What is a good graphing software ? The one that has the ability to accept an equation (linear, quadratic, etc.) from users and output a graph for that equation (software equivalnet of T1-84 graphing ...
7
votes
5answers
17k views

Determine third point of triangle when two points and all sides are known?

Determine third point of triangle (on a 2D plane) when two points and all sides are known? A = (0,0) B = (5,0) C = (?, ?) AB = 5 BC = 4 AC = 3 Can someone ...
11
votes
5answers
3k views

Why aren't the graphs of $\sin(\arcsin x)$ and $\arcsin(\sin x)$ the same?

(source for above graph) (source for above graph) Both functions simplify to x, but why aren't the graphs the same?
5
votes
1answer
180 views

How do you plot the graph of $y = \sin(x)+\cos(x)$ by converting it to another form?

Are there any trigonometric identity that can make it easier to plot?? I have no idea how it becomes a sin graph shape in the end.
4
votes
3answers
2k views

Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle

So why is it a function, even though for example $x = 8$; you'll have $y = +2$ and $y = -2$. It'll fail the vertical line test. But every textbook considers it as a function. Did I misunderstand ...
2
votes
1answer
130 views

How To Slice $Re(1/(1+z))$ Into A Cartesian Function For Any Angle?

The complex function $\frac{1}{1+z^2}$ may be broken into real and imaginary components: $$Re(\frac{1}{(1+z^2)})=\frac{1+x^2-y^2}{(1+x^2-y^2)^2+4x^2y^2}$$ ...
4
votes
2answers
311 views

Plotting graphs using numerical/mathematica method

From the author's equation 13, 14 We can write by inserting V''(A)=0, Solving for R we get, $$R= \frac{6^{D/4} \sqrt{D}}{\sqrt{-2^{1+\frac{D}{2}} 3^{D/2}+3 2^{1+D} A-3^{1+\frac{D}{2}} A^2}}$$ Now ...
2
votes
1answer
379 views

Calculating closest and furthest possible diagonal intersections.

Calculating closest and furthest possible diagonal intersections. Please refer to the image attached. It represents a $2D$ grid with the following properties: The grid origin is $(1,1)$ at the ...
27
votes
2answers
430 views

Is “imposing” one function onto another ever used in mathematics?

First of all, let me define what I mean by "imposing," and let me clarify that I've only studied this operation in 2D Euclidean space. Now then, to impose one function onto another, you need two ...
6
votes
6answers
5k views

Plot $|z - i| + |z + i| = 16$ on the complex plane

Plot $|z - i| + |z + i| = 16$ on the complex plane Conceptually I can see what is going on. I am going to be drawing the set of points who's combine distance between $i$ and $-i = 16$, which will ...
5
votes
4answers
14k views

How to find the angle between two straight line equations?

The Problem There are two straight lines with equations as follow y=-2x+10 and y=-3x+6 their point of intersection is (2,6) and i am asked to find the angle between them ? A detailed and easy ...
3
votes
2answers
49 views

How do you sketch the Poisson distribution function: $L(\mu;n)=\frac{\mu^{n}e^{-\mu}}{n!}$?

When doing a maximum likelihood fit, we often take a ‘Gaussian approximation’. This problem works through the case of a measurement from a Poisson distribution. The Poisson distribution results ...
3
votes
1answer
2k views

One algorithm for drawing graph of implicit function

All! Does anybody know who is author of algorithm described here and is the proposed solution correct?
2
votes
1answer
12k views

Boxplots and bar graphs

I'm studying for the GRE and came across several questions that I was unable to answer in a practice booklet, even after looking at the answer and trying to work backwards, and searching google and ...
1
vote
4answers
94 views

If the range of a function is $[a,b]$ ,where $a,b \in \mathbb N$ ,find $f(a+b)$.

Let $f(x)= (x+1) (x+2) (x+3) (x+4) + 5$ where $x \in [-6,6]$. If the range of this function is $[a,b]$ ,where $a,b \in \mathbb N$ ,find $f(a+b)$. ATTEMPT: Sketching the graph the we know that ...
1
vote
5answers
362 views

“Plotting” an equation

I have an equation like $$ (x - a)^2 + (y - b)^2 = r^2 $$ that represents a circle. I need to "plot" it very basically with a programming language. Computer graphics coordinate generally use the ...
2
votes
2answers
67 views

Help me conclude a statement about two points given the following…

Two points on the graph of $y=kx^p$ are labeled $A$ and $C$. Point $A$ has coordinates $(a,b)$, where $0<a<1$ and point $C$ has coordinates $(c,d)$, where $1<c$. If we are told that that the ...
2
votes
4answers
194 views

Function generation by input $y$ and $x$ values

I wonder if there are such tools, that can output function formulas that match input conditions. Lets say I will make input like that: $y=0, x=0$ $y=1, x=1$ $y=2, x=4$ and tool should ...
2
votes
4answers
307 views

Solving a quadratic Inequality

My question is: Solve $$9x-14-x^2>0$$ My answer is: $2 < x < 7$ Though I know my answer is right, I want to know in what ways I can solve it and how it can be graphically represented. ...
1
vote
3answers
66 views

Rotate the graph of a function?

How do I rotate a graph of a function around a point, and show it in the related equation? An example could be $f(x)=\lvert x\rvert$ (absolute Value) and $f(x)=x^2$
1
vote
2answers
301 views

Number of solutions of an arithmetic function's equation

Say, an equation is given below \begin{equation} 2\pi(x) - \pi(2x)=\omega(x) \end{equation} where $x$ is a positive integer, $\pi(x)$ is the prime-counting function, and $\omega(x)$ is the number of ...
1
vote
2answers
64 views

Graph of the function $[\frac{1}{x}]$

I'm interested in the graph of the function $[\frac{1}{x}]$. may seems simple, also I graphed it myself. But there is difference between my solution and the manual solution. Here is the solution of ...
1
vote
3answers
454 views

Plot of x^(1/3) has range of 0-inf in Mathematica and R

Just doing a quick plot of the cuberoot of x, but both Mathematica 9 and R 2.15.32 are not plotting it in the negative space. However they both plot x cubed just fine: ...
0
votes
2answers
146 views

Is this function $f(x)=x^{-1/3}$ continuous, when $x$ varies from $-1$ to $1?$

I have doubt ! regarding to this question , Is this function $f(x)=x^{-1/3}$ continuous, when $x$ varies from $-1$ to $1?$ As I read, when left limit is not equivalent to right limit ...
0
votes
2answers
71 views

Please guide me to draw this : graph of $x \geq 5$ and $y \geq 5$

how can I draw the graph for this the graph of $x \geq 5$ and $y \geq5$ is? please guide me to draw it thanks in advance
0
votes
1answer
44 views

Estimate growing graphs

Lets make my scenario not generic just so that i could use particular terms Say i have a graph of population per year of someplace over some decades Lets say the graph is like this How can i ...
27
votes
2answers
8k views

Cannabis Equation

How can an equation for the following curve be derived? $$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$ (From WolframAlpha)
34
votes
3answers
1k views

Why does the graph of $e^{1/z}$ look like a dipole?

I was looking at the color wheel graph of $e^{1/z}$, and my girlfriend commented that it looked just like a dipole. Does anyone have an explanation for that, why the geometry would be so similar? I ...
21
votes
11answers
5k views

What equation produces this curve?

I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline. The spline is pretty simple - a gentle curve which begins and ...
14
votes
3answers
8k views

Best software to take math notes?

I have read some old discussions about this topic and would like to get some up-to-date advice, if possible. How can I take math notes, write formulas and draw graphs on my pc (win 7), the easiest ...
8
votes
1answer
2k views

Very interesting graph!

I found a VERY interesting graph on http://www.xamuel.com/graphs-of-implicit-equations/. It looked very, very cool, but the equation of the graph is so simple! Here is the image of the graph: My ...
24
votes
1answer
738 views

Moriarty's calculator: some bizarre and deceptive graphical anomalies

Background: This is a problem I first came across a few years ago in a calculus textbook (a James Stewart one), where it addressed some of the pitfalls of using graphing calculators. The original ...
16
votes
13answers
2k views

How to explain the perpendicularity of two lines to a High School student?

Today I was teaching my friend from High School about linear functions. One of the exercises we had to do was finding equations of perpendicular and parallel lines. Explaining parallel equations was ...
5
votes
6answers
4k views

Why is the second derivative of an inflection point zero?

I wanted to know why is that so. I am just lost and want a detailed explanation.
4
votes
2answers
6k views

How do I determine the increasing order of growth of a set of functions?

I've been struggling with a homework-like problem (I'm a self-studier) and having trouble understanding the 'hints' I've already received. Please forgive my lack of knowledge around terminology. ...
9
votes
2answers
1k views

Draw graph of $\frac{1}{f(x)}$ from graph of $f(x)$

If I know the graph of $f(x)$, how do I draw the graph of $\frac{1}{f(x)}$?
8
votes
2answers
6k views

What is a function to represent a diagonal sine wave?

I need to be able to plot pixels in this pattern. To me, it looks like a sine wave pattern that is both diagonal and convergent. What would a function for that look like? Thanks.
5
votes
1answer
723 views

How can we describe the graph of $x^x$ for negative values?

We usually only see the graph $y=x^x$ for $x>0$, because $x^x$ is a complex number for most negative values of $x$. Yet here is a full graph of $y=x^x$ on the real line: This graph may seem like ...
4
votes
1answer
996 views

Can you write a non-piecewise equation that describes an arbitrary shape?

This batman equation thing got me thinking: for an arbitrary curve drawn on the Cartesian plane, can you write a corresponding equation which is not piecewise? What about closed shapes, a la the ...
3
votes
2answers
65 views

How do I rate smoothness of discretely sampled data? (Picture!!!)

In the sense that the following curves pictured in order will be rated 98%, 80%, 40%, 5% smooth approximating by eye. My ideas: (1) If the curves all follow some general shape like a polynomial ...
2
votes
2answers
250 views

Formula for solving for Cx and Cy…

I'm trying to create a formula to find the third point in a triangle based on two known points and three known sides. Known Sides: $AB, BC, AC$ Known Points: $A(x, y), B(x, y)$ Unknown Points: ...
2
votes
0answers
187 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 ...