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
votes
11answers
406k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
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 ...
28
votes
2answers
453 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 ...
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)
25
votes
4answers
1k views

Plot of a … Square?

Well there are equations which can plot a square like : $|x-y|+|x+y|=a$ But how about this equation: ? (At the end ... bear with me!) [Here I have taken $a = 1$] Plot of $$x^2 + y^2 = a^2$$ ...
25
votes
1answer
743 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 ...
24
votes
1answer
1k views

What is the flaw in my thinking for the graph of this function?

Consider the map $$ f: \mathbb R^2 \to \mathbb R, (x,y) \mapsto x^3 + y^3 + xy$$ This defines a surface in $\mathbb R^3$. Let's consider some level set $f(x,y) = c$: (see here page 67) I think ...
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 ...
19
votes
14answers
28k views

Piecewise functions: Got an example of a real world piecewise function?

Looking for something beyond a contrived textbook problem concerning jelly beans or equations that do not represent anything concrete. Not just a piecewise function for its own sake. Anyone?
19
votes
3answers
1k views

What do bitwise operators look like in 3d?

The hypothetical relation is $z = \mathrm{xor}\left(x,y\right)$ where xor is any bitwise operator such as AND, OR, NAND, etc. I see that these operations may be defined for integers trivially using ...
19
votes
3answers
325 views

When are graphs deceiving?

What are some examples of functions or quantities relating to functions (e.g., limits) $f:A \to B$ where $A$, $B \subseteq \mathbb{R}$ that require by-hand, "analytical" methods for analysis which are ...
18
votes
1answer
469 views

Mathematical Quine

I have recently discovered that I can create letters and any shape I want by hiding parts of curves by making them complex. To generalise if I want $x>a$ then I multiply my function by $\sqrt{\frac{...
17
votes
4answers
929 views

How many steps would it take at least to create a chessboard?

Imagine you have a 8x8 completely white field of squares on your screen. Now you can click on any square. When you do this, all the squares in that column and line (including the one you clicked on it)...
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 ...
16
votes
5answers
2k views

When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right \}=ax+b|x|+c$...
15
votes
3answers
225 views

Plotting $\left(1+\frac{1}{x^n}\right)^{x^n}$.

When I plot the following function, the graph behaves strangely: $$f(x) = \left(1+\frac{1}{x^{16}}\right)^{x^{16}}$$ While $\lim_{x\to +\infty} f(x) = e$ the graph starts to fade at $x \approx 6$. ...
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 ...
14
votes
1answer
249 views

Twin Primes (continued research)

This has become increasingly crowded, so at the onset, let me state this: My question is, is there some reason this is so linear that I'm not seeing? The only thing it seems to indicate to me is that ...
13
votes
8answers
420 views

How do I transpose an ellipse function to stretch the ellipse into curved space?

I'm working on an engineering project, using CAD software. I can write simple parametric functions to draw an ellipse, with $\theta$ ranging from $0$ to $2\pi$ radians:$$x=3.75\cos\theta$$$$y=1.25\...
13
votes
3answers
630 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
11
votes
2answers
6k views

Plotting in the Complex Plane

I just wonder how do you plot a function on the complex plane? For example,$$f(z)=\left|\dfrac{1}{z}\right|$$ What is the difference plotting this function in the complex plane or real plane?
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?
10
votes
1answer
664 views

Question regarding calculus, graph of functions, point of inflection.

We're studying the application of derivatives in mathematics right now. This refers to a question which arose in my head while solving a particular problem. The problem was: A function $f(x)$ is ...
10
votes
2answers
243 views

Is this graph based on rationals familiar?

Has anyone come across a graph like this? The black circles represent rationals in $(0,1)$ and their heights are roughly proportional to the reciprocal of the square of their lowest terms ...
9
votes
9answers
5k views

examples of functions with vertical asymptotes in real life

As a math teacher, I tend to get the class involved by finding real-life applications of the math- with functions and vertical asymptotes I am having trouble finding simple enough (rational) functions ...
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 $\frac{1}{f(x)}$?
9
votes
3answers
613 views

For how many functions $f$ is $f(x)^{2}=x^{2}$?

How many functions $f$ are there that satisfy $f(x)^{2}=x^{2}$ for all $x$? My text (Spivak's Calculus; chapter 7 problem 7) asks this question for continuous $f$, for which the answer is, of course ...
9
votes
2answers
262 views

How do I find, algorithmically, which parts of a given function are interesting to graph?

I'm building a program that does 2D graphing, and was wondering: How can I determine the default zoom level and x/y extents to display on screen, in such a way as to maximise the 'interesting' parts ...
8
votes
2answers
694 views

Roots of ln of a square

Problem: $$ y=\ln((3x-2)^2) $$ State the domain and the coordinates of the point where the curve crosses the x-axis At first sight, you say that the domain is $x>\frac23$ because $\ln$ is ...
8
votes
2answers
7k 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.
8
votes
3answers
164 views

Why does $\sin(\cos x)=\cos(\sin y)$ result in a lattice of circles?

Using Desmos graphing, I made an equation $\sin(\cos x)=\cos(\sin y)$ (here) which resulted in a strange lattice of symbols. I know that the trigonometric functions relate a triangle's sides to its ...
8
votes
4answers
26k 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 ...
8
votes
5answers
16k 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 can'...
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 ...
8
votes
1answer
100 views

Why does the plot of the legendre symbol of $x^2 - y^2$ over a finite field look rectangular

The small top-left thing is a plot of the legendre symbol of $x^2 - y^2$ over $\Bbb F_{37}$. The thing in the middle is plot for $\Bbb F_{587}$. The thing on the right is a plot of the legendre symbol ...
7
votes
2answers
3k views

Do odd functions pass through the origin?

An odd function is symmetrical in the 1st and 3rd quadrants. Does this means that it always passes through the origin?
7
votes
5answers
855 views

What do polynomials look like in the complex plane?

I have a hard time visualizing the fundamental theorem of algebra, which says that any polynomial has at least one zero, superficially I know this is true as every polynomial must have either an ...
7
votes
3answers
652 views

how do you graph a function?

I know techniques from calculus to more or less know the behavior of a function. But I still don't know how to graph functions people expect me to graph, for example, in Fulton's curve book there are ...
7
votes
5answers
295 views

Graphing $x^{3 / 2} + y^{3/2} =1$

My brother asked me what I thought was a fairly straightforward question, graph the function below over the real numbers: $$ x^{3/2} + y^{3/2} = 1.$$ Now of course, we can't have any negative ...
7
votes
3answers
203 views

How to visualize $f(x) = (-2)^x$

Background I teach Algebra and second year Algebra to middle school students. We are currently studying Exponential, Power, and Logarithmic functions. We study exponential functions (of the form $f(x)...
7
votes
4answers
8k 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
4answers
236 views

Graphing $x^{2/3}$: a question of domain

I'm trying to graph $x^{2/3}$. If I enter $y=x^{2/3}$, my graphing program excludes negatives from the domain: However, if I enter it as either $y=\sqrt[3]{x^2}$ or $y=(x^{1/3})^2$, it includes the ...
7
votes
5answers
18k 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 ...
7
votes
1answer
1k views

How do I plot multi case function in wolfram or geogebra?

How do I plot the following multi case function in wolfram or geogebra? $$ \begin{eqnarray*} f(x) = \begin{cases} 1, &\text{if }x \text{ is an integer}, \\ 0, &\text{if }x \text{ is ...
6
votes
3answers
516 views

Absolute value graph sketching

Where would you start if you were told to plot: $$||x-1|-1|$$ I looked at just $f(x) = |x-1|$ and noticed that the two equations are: $\pm (x-1)$ for $x \geq 1$ and $x < 1$. Extrapolating then: $\...
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 ...
6
votes
3answers
1k views

Why is wolfram alpha plotting this differently?

I have an equation for a cylinder as $x^2+(y-b)^2=a^2$ for some $a$ and $b$. so I just plugged in $b=2$ and $a=1$ and tried to plot it using wolfram alpha, and the 3D plot looked like half a cylinder, ...
6
votes
1answer
205 views

When is the sum of first $n$ numbers equal to the sum of the next $k$ numbers?

When is the sum $1+2+\cdots + n = (n+1) + (n+2) + \cdots +(n+k)$? The easiest solution $(n,k)$ is $(2,1)$. For example, $1+2 = 3$. Do any others exist? Roots of $(n+k)^2 + (n+k) = 2n^2 +2n$ give ...
6
votes
1answer
3k views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...