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Questions tagged [graphing-functions]

For questions regarding the plotting or graphing of functions. For questions about the kinds of graphs with vertices and edges, use the (graph-theory) tag instead.

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Plotting 3x3 rotational matrices and improper rotations

I'm trying to find a good visualization for my students to help them understand 3x3-rotation matrices and improper rotations. They are tasked to solve the following two exercises (there's a bit more ...
Zedssad's user avatar
  • 718
1 vote
2 answers
96 views

Is there an error in the Wikipedia graph of $\frac{\sin x}x$?

I was reading about the "sinc function" on Wikipedia and found the following graphs of $\dfrac{\sin x}x$ and $\dfrac{\sin(\pi x)}{\pi x}$. Part of the normalized sinc (blue) and ...
Soheil's user avatar
  • 6,794
0 votes
0 answers
8 views

Characterising the nature of Eigen values of a given paramteric matrix

question: A{2x2} = https://files.oaiusercontent.com/file-rZmIDJV1d2325YK6eQfPFTo1?se=2024-07-18T09%3A30%3A45Z&sp=r&sv=2023-11-03&sr=b&rscc=max-age%3D299%2C%20immutable%2C%20private&...
Ysh's user avatar
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0 answers
23 views

Density or growth rate for Eisenstein integers by products and doing $2 x + k$

Consider these two sets of Eisenstein integers. SET 1 : constructed by these rules : a) any unit is in the set. b) if $x$ is in the set, then so is $2 x + 7$. c) if $x$ and $y$ are in the set then so ...
mick's user avatar
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0 votes
1 answer
60 views

How to visualize triangle using a software

How to visualize (using some plotting software) the triangle inequality, $|x-z|\le|x-y|+|y-z|$, where $x,y$ and $z$ belong to some finite intervals. I am asking for general way, for example, $(x-z)^2\...
stephan's user avatar
  • 375
6 votes
0 answers
82 views

Is the area enclosed by p(x,y) always irrational?

Take a polynomial $p \in \mathbb{Q}[X,Y]$. Now draw the graph of $p(x,y)=0$. If, like $X^2-Y^2-1$, this turns out to enclose a finite area, is the area enclosed always irrational? There are some ...
Zoe Allen's user avatar
  • 5,633
2 votes
0 answers
78 views

Lucas numbers in polar coordinates: why does this monstrosity of a graph happen?

The other day I've been bored and was messing around in Desmos. I've had a silly idea: what kind of spiral would I get if I put down Fibonacci or Lucas numbers in polar coordinates? I've plotted a ...
Stepanchicko's user avatar
-1 votes
3 answers
86 views

Is there an elegant method to find whether the graph is symmetrical or not

For example, Let us consider a function, say, $f(x)=\frac{1}{1+tan^{\sqrt 2}x}$ This cannot be computed when it is indefinite. But, this can be integrated when we try to compute it with definite ...
Rishwanth S V's user avatar
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2 answers
44 views

How to plot a ray intersecting a point uniformly between two rays?

I have two rays and a point. I need to dynamically plot a new ray which has an origin placed uniformly in-between that of the other two ray origins and which also intersects the point. For instance, ...
Harper Rhett's user avatar
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0 answers
33 views

Doubt on graph of indefinite integration starting from 0 instead of $-\infty$

The graph of integration of a function show us the area under the function. If we specify the range of integration we plot the graph between the range. So if we just use indefinite integration we ...
Rishwanth S V's user avatar
0 votes
1 answer
25 views

Question on exponential functions and drawing suitable lines on the graph

This question is from an exercise in an Edexcel Further Pure Mathematics book. Parts a, b, and c were fairly easy for me. For part a, I found the corresponding values of y using a calculator and in ...
Tanish Shukla's user avatar
1 vote
5 answers
57 views

Function $f$ is defined by $f(x)=-x^2$. Function $g$ is obtained by reflecting the graph of $f$ across the line $y=1$. Find $g(4)$

I have the answer, but I am interested in the process by which it is obtained because in the textbooks I've used, they tend not to have questions such as this one. I find this question rather tricky. ...
David A.'s user avatar
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0 answers
24 views

Can't bring the graph higher on the y-axis

The goal is to get a slowly decreasing function where x is between -0.2 and 0, and y is between 1 and 1.2. I've plotted this formula in Python: \begin{align}y=1−(\frac{x+1.5}{a})^n,\text{where a =0.01,...
codenoodles's user avatar
0 votes
3 answers
66 views

How can we draw $x(t)=3\sin(t) \sin(3t),y(t)=3\cos(t) \cos(3t)$? [closed]

I tried to take multiple values for $t$ but this was a painful procedure. I wondered if there is any way to make to graph $(x,y)$ faster. However, every way I tried failed to work. For example, ...
JOHN BOURAS's user avatar
1 vote
0 answers
62 views

Constructing a Curve from a Differentiable Function's Normal Lines at a Fixed Distance. [duplicate]

I've been experimenting with a graphing calculator and stumbled upon an interesting geometric construction involving functions and their normal lines. Here's the problem I'm trying to solve: Let's ...
pie's user avatar
  • 6,620
0 votes
0 answers
9 views

Torus Circle Meridian modification for Cassinian Intersections

Is it possible to define a torus whose sections parallel to torus axis are Ovals of Cassini? For contextual reference sections of a Circular Torus and code (Mathematica) are given below: We can see ...
Narasimham's user avatar
  • 41.1k
3 votes
1 answer
192 views

Graph of the functions for a system of two equations

I'm a master student in Economics, and I'm going through a paper which involves some mathematics. I'm gonna try to make the argument as far as possible from economics. Consider the following system of ...
Maximilian's user avatar
0 votes
2 answers
36 views

Logarithm approximation loses solution

I was doing an exercise in which I had to plot by hand a function. The function was $$f(x)=\ln\left(\frac{\sqrt[3]{x}}{3x - 1}\right)$$ which I rewrote into $$f(x)=\frac{\ln\left(x\right)}{3} - \ln\...
serax's user avatar
  • 135
-2 votes
2 answers
34 views

Horizontal asymptote of a Rational Function [duplicate]

I didn't quite understand how the horizontal asymptote of the function $r(x) = \frac{3x^2 - 2x - 1}{2x^2 + 3x - 2}$ can be $\frac{3}{2}$, since when you use desmos, for example, to graph it, part of ...
Guilherme Cintra's user avatar
2 votes
1 answer
218 views

Non-symmetric bump function

I am trying to create a smooth bump function $f(x;a,b,c,k_1,k_2)$ satisfying the following properties: $f$ is smooth (can be relaxed) $f$ is supported on $[a,c]$. $f$ is increasing on $(a,b)$. $f$ is ...
rd16's user avatar
  • 63
2 votes
3 answers
122 views

Finding $b$ such that $\dfrac{1}{\left(x - 2\right)^2} + b = -x$ has exactly two solutions, using a non-calculus approach

The question: Let $f(x) = \dfrac{1}{\left(x - 2\right)^2} + b.$ Find $b$ when $f(x) = -x$ has only two solutions. My attempt at a solution (without using any calculus): $$\dfrac{1}{\left(x - 2\right)^...
Elite's user avatar
  • 23
0 votes
2 answers
53 views

when drawing a graph, what does f(-x) = -f(x) mean?

The question I am working on is this: Sketch the graph of a function that satisfies all of the given conditions. Note that you need to make ONE graph that satisfies all the given conditions f'(x)>0 ...
jessie's user avatar
  • 1
1 vote
1 answer
61 views

Smooth approximation of the floor function

Question I am looking for a sequence of $C^\infty$ real functions $f_k(x)$ such that: $$\forall x\in \mathbb{R}:\lim_{k\rightarrow\infty}f_k(x)=\lfloor x\rfloor$$ If the $C^\infty$ condition holds ...
Soham Saha's user avatar
  • 1,392
0 votes
0 answers
53 views

General method to graph curves

I am looking for some "general" method to make the graph of a 2 dimensional curve. What I mean by general is a clear path as the one can take with functions: looking for some points where it ...
MiguelCG's user avatar
  • 345
1 vote
1 answer
69 views

How to see the graph of this? $n=\sin(x)\cos(y)+\sin(y)\cos(z)+\sin(z)\cos(x)$ [closed]

$$n \text{ (constant)} = \sin(x)\cos(y)+\sin(y)\cos(z)+\sin(z)\cos(x)$$ Code is this, but I can't emulate this. Why? Even WolframAlpha can't make graph too. ...
Myeongjun Chae's user avatar
0 votes
1 answer
32 views

How can I combine multiple functions into one to make a connected graph?

I tried this in desmos: $$ f\left(x\right)=\left(\left(x+6\right)\cdot\frac{\sqrt{-2-x}}{\sqrt{-2-x}}\right)+\left(x^{2}\cdot\frac{\sqrt{4-x^{2}}}{\sqrt{4-x^{2}}}\right)+\left(\left(\frac{x}{2}+3\...
DavidNyan10's user avatar
55 votes
6 answers
4k views

Regarding a Coin Toss Experiment by Neil DeGrasse Tyson, and its validity

In one of his interviews, Clip Link, Neil DeGrasse Tyson discusses a coin toss experiment. It goes something like this: Line up 1000 people, each given a coin, to be flipped simultaneously Ask each ...
Mystic Mickey's user avatar
2 votes
0 answers
58 views

Rotating an archimedean spiral

I'm trying to rotate an archimedean spiral in such a way that allows it to attach to another archimedean spiral without overlapping each other, kind of like the image here below: I've already ...
Jediweirdo's user avatar
1 vote
0 answers
53 views

$f(x)=\frac{x\lfloor x\rfloor}{1+x^2}$. Find range.

Find range of the function $f(x)=\frac{x\lfloor x\rfloor}{1+x^2}$. My Attempt: I found this problem really weird. On plotting the graph i observed that $f(x)$ is not able to take value between $0.5$ ...
Maverick's user avatar
  • 9,599
0 votes
2 answers
56 views

What function describes the curve created by these points? [closed]

When $n$ is even, the lines $n^x$ and $x^n$ cross three times. One of them is in the negatives. What is the function for the curve these intersects are on?
XtemeCJ's user avatar
  • 19
0 votes
1 answer
47 views

What is the explanation of these special cases of tangents [closed]

The graph $y = |x|$ has no tangents at $x=0$ since it is not differentiable at that point, but it is possible to draw an infinite number of tangents to the graph at $x=0$, so why does it technically ...
Doodieman360's user avatar
1 vote
0 answers
39 views

Confusion regarding the graph of half an ellipse

So, starting with $E:4x^2+y^2+8x-4y-8=0$, the ellipse is given by $\frac{(x+1)^2}{4}+\frac{(y-2)^2}{16}=1$. Then, solving for $y$, I got: $$y=\pm \sqrt{-4x^2-8x+12}-2$$ Maybe is a silly question, but ...
Roma_Rayado's user avatar
-1 votes
1 answer
71 views

Rotating a 2D function in 3D space [closed]

Suppose we are given a function $f(x)$ in the x-y plane. We add a z axis perpendicular to this plane and rotate the function 360 degrees about an axis $x=x_0$ (on the x-y plane) in this new 3-...
Faiyaz's user avatar
  • 11
1 vote
2 answers
78 views

Creating a function that acts differently in certain values of $x$

I'm trying to develop an increasing leveling system for a game that currently works according to the following formula: $d \cdot (ax^2 + bx + c)$ = health_in_current_level $d\;\Rightarrow$ base health ...
Metaldream's user avatar
9 votes
5 answers
2k views

Can a straight line be drawn through a single node on an infinite square grid without passing through any other nodes?

The problem is from an advanced 8th grade math curricula, and marked with a star: *The topic is "Real numbers" The plane is covered by an infinite square grid. Is it possible to draw a ...
curioushuman's user avatar
0 votes
2 answers
39 views

How do I move the origin of a logarithmic spiral?

Context: I'm a high school junior (in pre-calculus) and I'm trying to teach myself how to graph a logarithmic spiral for a math/art project. Basically, I need to move the center of a spiral from the ...
rotraptor's user avatar
0 votes
2 answers
55 views

Check injectivity for $f(x)=x+\sin(x)+7$; given that $f:\mathbb{R}->\mathbb{R}$

It was a homework problem. I know three ways of checking injectivity. All of which confuse me. One is the horizontal line test. That is, making the graph and checking for more than one point of ...
SAGE's user avatar
  • 11
3 votes
1 answer
94 views

The curves of the equation $\sqrt[y]{x} + \sqrt[x]{y} = n$ intersect at $n≈2.88933572$. Is there any significance to this number?

Please see this short, compact video for an understanding of what I mean. I'm not asking about the weirdness of taking the y-th root of x and the x-th root of y, my question is solely about the number ...
user267545's user avatar
4 votes
1 answer
186 views

What is the reason for these strange oscillations? Issue with Desmos?

Take a partition of $\Bbb R^2_{\gt 0}$ by the union of functions indexed by real $t\ge 0$ $$\mathcal F:=\bigg \lbrace \mathcal M[\chi_t(x)]\cup \mathcal M\bigg[\frac{1}{1-\chi_t(x)}\bigg] \bigg \...
zeta space's user avatar
0 votes
1 answer
30 views

Significance of tangent passing through the origin in graphical interpretation

(This question was asked in CSIR NET June 2019 examination) A monkey climbs a tree to eat fruits. The amount of energy spent climbing on the different branches has a relationship, as shown in the ...
S.S's user avatar
  • 1,239
0 votes
2 answers
69 views

What will be the equation as a function of x for this graph? [closed]

This is the graph: And I want to find what equation can plot this graph. I believe somehow trigonometric functions and fourier transform can do it. But don't know how.
in.yssh's user avatar
-1 votes
1 answer
49 views

Finding an equation for a series of non-linear points [closed]

I'm currently working on implementing the gain function (a function that applies contrast to an image) of ImageData (Open Office XML see https://schemas.liquid-...
Guilherme Lopes's user avatar
3 votes
1 answer
54 views

Defining a custom function

The Problem Define a function $f:\mathbb{R\times R\rightarrow R}$ which satisfies the following properties: $$\frac{\partial f(x,k)}{\partial x}=0\text{ at }x=0$$ $$\forall k\in\mathbb{R}:f(1,k)=1$$ $$...
Soham Saha's user avatar
  • 1,392
-2 votes
1 answer
51 views

Questions about functions and their graphs [closed]

I just have a few questions about function analysis that have been confusing me ever since we started learning about it, hope someone can answer them. When writing out a domain of a function, how do ...
umricky's user avatar
  • 11
1 vote
1 answer
42 views

General degree distribution of Soft Random geometric Graphs

I am interested in the degree distributions of Soft Random Geometric Graphs, and was wondering if anyone could give me some input. Soft RGG's are random graphs, which are constructed by first ...
Rowan Potato's user avatar
0 votes
1 answer
57 views

Hello, I am having trouble understanding why the graph of the function shifts to the right and not the left. [duplicate]

As you can see in this graph, there are equivalent points on functions g and f. The relation between $g$ and $f$ is $g(x) = f(x-2)$. As the $x$ value is decreased, why doesn't the graph move to the ...
Aarushi da Great's user avatar
0 votes
0 answers
26 views

The Graph of $f$ when evaluated at $y$.

The traditional Cartesian coordinate system is labeled as $y$ for the vertical axis and $x$ for the horizontal axis. Suppose we have a graph for $f(x)=cx$. When one evaluates $f(y)=cy$, it maps a ...
webtolight's user avatar
3 votes
2 answers
704 views

understanding logarithmic scale in a graph

I plotted the function $1000\sin{\frac{x}{1000}}$ on desmos and set it to the logarithmic scale but I am having trouble understanding the result which looks like this: Why does the graph go linear ...
Aarush Saharan's user avatar
3 votes
1 answer
38 views

Domain of a Graph That is Just a Horizontal Line with Points at the Beginning and the End.

I have a graph that is just a horizontal line with one full painted point at the beginning of the graph $x=0$ and one empty point at the end $x=10$. Would the correct answer for domain of this ...
Anon's user avatar
  • 43
0 votes
0 answers
19 views

Ideas for a function which generates a skewed random distribution plot

I am trying to figure out a function that can plot a curve similar to these ones: The area under the curve is 1, since this is a density plot. However, it doesn't look like I can fit a gaussian to ...
ValientProcess's user avatar

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