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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328
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10answers
357k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
29
votes
3answers
733 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 ...
26
votes
2answers
5k 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)
18
votes
1answer
377 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
13k 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
12answers
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 ...
13
votes
3answers
4k 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 ...
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
2answers
621 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
518 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
1answer
392 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
242 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
3k 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
2answers
3k 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?
7
votes
5answers
232 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 ...
6
votes
2answers
764 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?
6
votes
1answer
195 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
200 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
90 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 ...
6
votes
5answers
4k 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 $x$ ...
6
votes
1answer
504 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 ...
6
votes
1answer
182 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 ...
6
votes
1answer
830 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 ...
5
votes
2answers
365 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
140 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
5answers
133 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
267 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
3answers
387 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 ...
5
votes
4answers
133 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
3answers
728 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
3answers
12k 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
3answers
110 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 ...
5
votes
2answers
69 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
3answers
6k 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
4answers
168 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
4answers
179 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 ...
5
votes
1answer
42 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
2answers
100 views

How to graph equation

So the problem is to find all points $(x,y)$ on the real plane such that $f(x,y) = \cos^2(x+t) + 2\sin(x+t)\cos(y) - \frac{(\cos y - 1)^2}{2} - \sin(x) \lt .5$ for all real $t$. I'm not sure where to ...
5
votes
1answer
139 views

Finding a function that fits the “lowest points” of another one

I came up with this problem, which I cannot solve myself. Consider the function: $\displaystyle f(x) = x^{\ln(|\pi \cos x ^ 2| + |\pi \tan x ^ 2|)}$, which has singularities at $\sqrt{\pi}\sqrt{n + ...
5
votes
2answers
95 views

$P(P(\cdots(P(x))))$ and its integer solutions

Problem: Suppose that $P(x)$ is a polynomial with degree at least $2$ and integer coefficients. Let $Q(x)$ have the form $$ Q(x) = P(P(P(\cdots P(x) \cdots))) $$ for some finite number of nested $P$s. ...
4
votes
6answers
3k 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 ...
4
votes
2answers
502 views

Why does this graph intercept both axes at the golden ratio?

Earlier, I was playing around with the Desmos Graphing Calculator, and I discovered that the following formula intercepts both the x and y axes at the golden ratio. I know that it makes sense, but I ...
4
votes
5answers
280 views

How to graph/visualize complicated inequalities

I'm having trouble visualizing areas defined by for example, $$ x^2 + y^2 \leq 2y $$ Or $$ (x^2 +y^2)^2 \leq 2a^2(x^2 - y^2) $$ What is the thought process in picturing these regions?
4
votes
3answers
1k 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 ...
4
votes
5answers
252 views

A simple function equation

I come from a programming background and I can’t find a simple math function. The request might seem strange, but I needed it a graphical context to alter some points locations: I need a function ...
4
votes
5answers
173 views

Graphing $\sin(|x|)$?

I'm confused on how the graph is in both quadrant II and III. If $|x|$ is evaluated first wouldn't all the answers be positive, so that when the range of $|x|$ is plugged into $\sin$ wouldn't the ...
4
votes
4answers
7k 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 ...
4
votes
1answer
70 views

Is the graph of $ r = \dfrac{3 \pi}{5} $ a diagonal line?

I'm reviewing my notes and I came upon this. It says that $$ \begin{align} r \sin \theta &= 5 \tag{horizontal line} \\ r &= \dfrac{3 \pi}{5} \tag{diagonal line} \end{align}$$ How is this ...
4
votes
1answer
66 views

Find the absolute maxmium of the function $f(x) = x \cdot {e}^{-x}$

How can I find the absolute maximum of this exponential function? $f(x) = x \cdot {e}^{-x}$ I know that the first step is to take the derivative of the function, like so: ${f}^{\prime}(x) ...
4
votes
3answers
237 views

Sketching graphs : Most importaint points

I'm currently studying for a test which places a lot of emphasis on sketching graphs of certain functions, without anything but a ruler and a pencil. I mean tricky functions, for example: $y = ...