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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397
votes
11answers
407k 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 ...
4
votes
1answer
267 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 ...
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 ...
9
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 $x$ ...
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 = ...
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 ...
2
votes
3answers
351 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 ...
11
votes
5answers
4k 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?
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
133 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: $$Re(\frac{1}{(1+z^2)})=\frac{1+x^2-y^2}{(1+x^2-y^2)^2+4x^2y^2}$$ $$Im(\frac{1}{(1+z^2)})=\frac{-2xyi}{(1+x^...
2
votes
1answer
384 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 top-...
36
votes
3answers
2k 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
1answer
207 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.
1
vote
4answers
95 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 ...
8
votes
2answers
25k 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'...
3
votes
2answers
51 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 in ...
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
13k 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 ...
4
votes
2answers
312 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 ...
1
vote
3answers
473 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: ...
1
vote
2answers
302 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
3answers
71 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 $f(x)=x^2$
0
votes
2answers
72 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
45 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 ...
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 ...
22
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 ...
25
votes
1answer
752 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
5k 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. Let'...
3
votes
3answers
2k views

How to find the equation of the graph reflected about a line?

Consider the graph of $y = e^x$ (a) Find the equation of the graph that results from reflecting about the line $y = 4$. (b) Find the equation of the graph that results from reflecting about ...
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
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.
5
votes
1answer
764 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
1k 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
96 views

The graph of the function $f(x)= \left\{ \frac{1}{2 x} \right\}- \frac{1}{2}\left\{ \frac{1}{x} \right\} $ for $0<x<1$

Let for reals $$\{x\}=\text{Frac}(x)$$ the fractional part function, take for example the more common definition, the first (there is a different definition as you see in this MathWorld's Page, ...
3
votes
2answers
66 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
275 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: $C(...
2
votes
0answers
199 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 ...
2
votes
1answer
515 views

Find equation of ellipse given two tangent lines at given points and a point on ellipse

I'm attempting to generate an ellipse for a stair simulation game of mine, and the inputs are: A point on the ellipse The slope of the tangent line to the ellipse at that point Another point ...
8
votes
5answers
892 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
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)...
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 ...
5
votes
2answers
416 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.