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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358
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10answers
373k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
30
votes
3answers
928 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 ...
27
votes
2answers
6k 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)
24
votes
4answers
916 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 $$x^2 + y^2 = a^2$$ ...
23
votes
1answer
666 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 ...
20
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 ...
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 ...
18
votes
1answer
424 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 ...
17
votes
14answers
17k 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?
14
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 ...
14
votes
3answers
5k 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 ...
13
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 ...
11
votes
5answers
2k 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?
9
votes
9answers
2k 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
794 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
545 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
4k 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?
9
votes
1answer
494 views

Doubt 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 ...
9
votes
2answers
244 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
4k 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
1answer
1k 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
2answers
220 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 ...
8
votes
1answer
83 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 ...
8
votes
0answers
91 views

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

First of all, let me define what I mean by "imposing." Basically, I mean graphing some function with respect to some other function, rather than with respect to the x-axis. To be more specific, for ...
7
votes
2answers
1k 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
411 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
5answers
209 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
168 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 ...
7
votes
5answers
8k 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 $x$ ...
7
votes
1answer
984 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
485 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 ...
6
votes
1answer
203 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
4answers
212 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 ...
6
votes
3answers
139 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 ...
6
votes
4answers
9k 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 ...
5
votes
6answers
4k 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
2answers
384 views

What function has a graph that looks like this?

I delete my file which I used to produce this graph. Does anybody have some idea how to produce it again? Thanks for a while.
5
votes
4answers
147 views

Visualization of a set

How can I imagine the set $$ M:=\left\{(x,y,z)\in\mathbb{R}^3:z=xy\right\}? $$ Is there a program that can visualize that?
5
votes
4answers
341 views

Drawing a graph that is flat, but then spikes

I'm trying to create a function that makes a graph like this: ...
5
votes
5answers
156 views

Points on $(x^2 + y^2)^2 = 2x^2 - 2y^2$ with slope of $1$

Let the curve in the plane defined by the equation: $(x^2 + y^2)^2 = 2x^2 - 2y^2$ How can i graph the curve in the plane and determine the points of the curve where $\frac{dy}{dx} = 1$. My work: ...
5
votes
4answers
4k 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 ...
5
votes
3answers
16k 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 ...
5
votes
4answers
141 views

Sketch the function $y = {1 \over {{x^2}}}\ln x$

I don't know where to begin with this, the ${1 \over {{x^2}}}$ part of the function throws me off, how to do I go about this? How does one generally approach a question like this?
5
votes
4answers
10k 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 ...
5
votes
3answers
930 views

Why graph a function?

Please enlighten me as to how graphing a function helps. I can see a graph's utility with simple functions as they instantly give you value of dependent variable. But ignoring them and considering ...
5
votes
2answers
205 views

How to graph this sin equation?

I have the following sin equation which I am supposed to graph: sin(3x) = -1 and also find how many solutions it contains ...
5
votes
2answers
109 views

Intuitive characterization of the graph of a twice differentiable function

In high school textbooks, the following characterizations are often found: A function is continuous if its graph can be drawn without lifting the pencil. and A function is differentiable if ...
5
votes
4answers
181 views

How can a point of symmetry have a slope which isn't either $0$ or $±\infty$?

I've got a bit of a doubt with a question I'm solving. It goes like this: For $a>0$, let $f:[-4a,4a] \to R$ be an even function such that $f(x) = f(4a - x) \hspace{2 mm}\forall x \in [2a, ...
5
votes
1answer
50 views

Graph of $0 = \frac{x^2 -y}{y^2-x}$

When you plot this equation implicitly, you get something really weird. You can see $x^2 - y = 0$ in there, but why do you see a noisy $y^2 - x = 0$ on the side? My guess is that it is a rounding ...
5
votes
4answers
207 views

Formula with 2 points of inflection

$x^3$ has a point of inflection at $x=0$. How will you modify the formula to add a 2nd point of inflection at $x=1$? Plot of $x^3$ Plot of $x^3(x-1)^3$ Update The plot I am aiming to achieve ...