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

learn more… | top users | synonyms (2)

322
votes
10answers
347k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
26
votes
3answers
646 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 ...
25
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
366 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 ...
14
votes
12answers
10k 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
3k 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
1k 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
520 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
496 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
330 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
238 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
2k 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
2k 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?
6
votes
1answer
192 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
187 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
5answers
2k 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
210 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
736 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
450 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?
5
votes
2answers
347 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
5answers
119 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
239 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
339 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
128 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
624 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
10k 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
161 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
160 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
135 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
94 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. ...
5
votes
1answer
168 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 ...
5
votes
0answers
62 views

Triangle mapped on a sphere in $\mathbb R^3$? [closed]

How can I map a triangle on an sphere? I want to visualize (plot or animate) it for my student in my Non Euclidean geometry. I have no restrictions on the triangle's kind or on the sphere in $\mathbb ...
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
4answers
122 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?
4
votes
3answers
884 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
154 views

Graphing $\sin(|x|)$?

I'm confused on how the graph is in 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 range of ...
4
votes
4answers
5k 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
67 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
4k 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 ...
4
votes
3answers
157 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 = ...
4
votes
2answers
795 views

Slope of a nonlinear curve at a single point

This part of my microeconomics lesson plan has me baffled. Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
4
votes
1answer
1k views

Finding out a rational equation via a graph

I need to be able to find an equation from this graph So far I have this graph with the equation $-1/((x-3)^3)$ I can see from the desired graph that there is no horizontal asymptote, compared ...
4
votes
1answer
60 views

How can I determine the shape of a graph with $x^2$, $x$, and $y^2$ terms?

I'm working through a multivariable calculus course. I'm ~5 years removed from my most recent calculus course, and ~10 years removed from my most recent trigonometry course. While I'm understanding ...
4
votes
1answer
47 views

Speediness and correctness when graphing by hand .

First of all thank you for visiting this question! I believe it's a pretty simple problem but get's kinda hairy and time consuming on each step as I have done it, so my question (the one you are here ...
4
votes
2answers
52 views

find a function such that it is symmetric across $y=1-x$ passing through $(0,0)$ and $(1,1)$, (not homework)

I am attempting to characterize a specific type of function. The function would be such that it is symmetric across the line $y=1-x$ This function would be a mapping $f:[0,1]\rightarrow [0,1]$ such ...
4
votes
2answers
287 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 ...