# 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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### 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 ...
10 views

### There exist a path of length $\chi(G)$ - 1 in a connected graph G

For any undirected connected graph G, let $\chi (G)$ be its chromatic number. Then for every vertex v in G, there exists a path of length $\chi (G)$ - 1 starting from v. My approach : for any vertex ...
37 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 $0.5$ ...
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### Looking for similar trigonometric functions

Has anyone seen such a function before? I am not looking for the exact formula, but rather the type or structure of such a function. I.e. I would be happy to see the explicit formula of a function ...
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### Using the Airy Function to give a solution to a differential equation [closed]

Questions (b) to (e) attached How do I solve part (e)? It says to use the Airy Function and its derivative to give a solution to the differential equation but I am really unsure as how to proceed. ...
54 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?
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### 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 ...
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### Plot request $\zeta_5(s) = \sum_{a>-1} \sum_{b>-1} \frac{1}{(a^2 + 5 b^2)^s}$ and $\zeta_{17}(s) = \sum_{a>-1} \sum_{b>-1} \frac{1}{(a^2 + 17 b^2)^s}$

Let $$\zeta_5(s) = \sum_{a>-1} \sum_{b>-1} \frac{1}{(a^2 + 5 b^2)^s}$$ $$\zeta_{17}(s) = \sum_{a>-1} \sum_{b>-1} \frac{1}{(a^2 + 17 b^2)^s}$$ omitting division by $0$ ofcourse and using ...
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### Seeking Guidance on Numerical Approximations and Graphical Tools. [closed]

I am a self-learner who likes pure mathematics. I always want to try new things and see where they will lead me, but in most cases, they involve a lot of complicated calculations. For example, in A ...
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1 vote
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### 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 ...
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### 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-...
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1 vote
69 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 ...
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 ...
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### 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 ...
49 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 ...
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### 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 ...
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### 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 ...
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1 vote
31 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 ...
55 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 ...
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 ...
692 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 ...
29 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 function be ...
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### 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 ...
148 views

### Find the set of values of $\alpha$ so that $f(x)=\dfrac{\alpha x^2+6x-8}{\alpha+6x-8x^2}$ is one one.

Let $f$ be a function defined in its domain given by $f(x)=\dfrac{\alpha x^2+6x-8}{\alpha+6x-8x^2}$. Find the set of values of $\alpha$ so that $f(x)$ is one-one. My attempt As $f(x)$ have to be one-...
57 views

### Randomly Generating Real-Rooted Polynomial Equations

I need a simple function to generate real-rooted polynomial functions to demo my Desmos Aberth-Ehrlich rootfinding implementation. My current function is as follows: Let $n \in \mathbb{Z}^+$ be the ...
1 vote
70 views

### Is $y = (\log x)^u$ faster than $y = x$ for any $u$?

If $(\log x)^u\over x$ converges to a constant as $x \rightarrow \infty$, then the set $S$ of possible values of $u$ is (A)$[-1,1]$ (B)$(-\infty,1]$ (C)$(-\infty,\infty)$ (D)None of the above Here's ...
1 vote
$(-2)^3=-8$ and $(-2)^2=4$, right? And $-(2^3)=-8$ and $-(2^2)=-4$. So that means $(-a)^x$ does not equal $-(a^x)$. My question is why do we never see graphs of $(-a)^x$ then?? I tried graphing $(-2)^... 0 votes 0 answers 6 views ### Any good applications to graph a Cartesian Coordinate 3D plane with the Z axis as imaginary? Apologies if this is confusing or worded incorrectly. I would like a graphing application that can graph in the 3D plane with real numbers on the X and Y axis and imaginary numbers on the Z axis. Does ... 1 vote 0 answers 52 views ### Is$f(x):=\lim\limits_{n \to \infty }(n!)^x \prod\limits_{k=1}^n \frac{k!}{(k+x)!}$a Gaussian curve? In this question I was trying to generalise the gamma function and defined$f(x+1)= g(x+1)f(x)$for some function$g$such that$g$is eventually non negative function, To make it clear that$f$... • 5,465 0 votes 2 answers 51 views ### exponential graphing with intercept [closed] I'm not sure what to do exactly. I got the equation of the line to be$y=\dfrac{p}{\ln\left(p\right)}x+p$is this correct? Now I need to solve for x using the above. 0 votes 0 answers 30 views ### plot3d hyperelliptic singular curve I am trying to draw a singular hyperelliptic curve of genus two in Sage. My goal is to obtain something that looks like (including the oriented one-cycles): I think that the equation of such a ... • 3,210 0 votes 0 answers 23 views ### Morse theory graphic How can I make the images that appear in Morse theory?. Type Beginner's question about homotopy type in Milnor's Morse Theory, i try in geogebra but i cannot. 1 vote 0 answers 73 views ### How to graph the antiderivative of Weierstrass function:$f(x)= \sum\limits_{k=0}^ \infty \frac{\cos\left(13^k\pi x \right)}{2^k}$. The Weierstrass function:$f(x)= \sum\limits_{k=0}^ \infty a^k {\cos\left(b^k\pi x \right)}$where$0<a<1, \ b \in 2\mathbb{N}-1, \ ab > 1+\frac{3\pi}{2}$is an example of a continuous ... • 5,465 1 vote 2 answers 259 views ### Find the number of solution(s) of equation$f(x)=2^x-x^2+x+\cos x$Question: Find the number of solutions of equation$f(x)=2^x-x^2+x+\cos x=0$Given answer is$1$My Attempt I have checked the derivative of it. $$f'(x) = 2^x\ln2-2x+1-\sin x\\f''(x)=2^x(\ln2)^2-2-\... 0 votes 0 answers 23 views ### Method to find a type of equation that can fit a particular shape? I'm trying to find a mathematical expression for a function that can fit this kind of data: I wonder if there is a better way to do it than the naive high-order polynomial fit. It seems like there is ... 0 votes 1 answer 56 views ### How to find exact Riemann-Sum? I have been given this rather simple looking assignment, which is confusing me a lot. Given is: f:[0,5] \rightarrow \mathbb{R} where f(x)=2x+3. The first thing I had to do, was to determine the ... • 31 0 votes 0 answers 27 views ### How to plot two seperate sequences in one plot such that there difference is clear? Suppose I have two sequences a_n and b_n. They both start from a very high number say 25000 and converges to zero. If I plot them in one plot, as they start from a very large number, the plot ... • 361 5 votes 0 answers 84 views ### Desmos not plotting the obvious inequality correctly? [closed] I was checking the subadditivity of the function f\colon x\mapsto \min(1, x), i.e., whether f(x + y)\le f(x) + f(y) and was expecting that the entire first quadrant would be colored. However, the ... • 3,973 0 votes 1 answer 26 views ### Formula for minimum of a changing parabola So what I want to find out is the path drawn by the parabola y=x^2+bx minimum as b changes. Im pretty sure it draws an upside down parabola because if I put in Desmos and slide the b it goes in the ... • 23 2 votes 4 answers 125 views ### Graphing (\lfloor x \rfloor + \lfloor1-x\rfloor) \lim_{x\to0+}(\lfloor x \rfloor + \lfloor1-x\rfloor) \lim_{x\to0-}(\lfloor x \rfloor + \lfloor1-x\rfloor) I tried to solve by graphing (\lfloor x \rfloor + \lfloor1-x\rfloor) Graph of the ... • 35 0 votes 2 answers 59 views ### Number of continuous points of a graph (Problem 34 from 97-99 Math GRE practice questions booklet) Problem Statement: Let f be a function with domain [-1, 1] such that the coordinates of each point (x, y) of its graph satisfy x^2 + y^2 = 1. What is the total number of points at which f ... • 79 0 votes 0 answers 17 views ### Graphing dy/dx of a parametric equation. Consider the first quadrant of a circle. We can represent the first quadrant of a circle as: y_1 = \sqrt{1-x^2}, such that 0\leq x \leq 1 \\ and in parametric terms as: \left(\frac{1-t^{2}}{1+t^{... • 125 0 votes 1 answer 53 views ### What is the graph of Rudin's 7.18 function Code borrowed from here Theorem 7.18 from Baby Rudin: There exists a real continuous function on the real line which is nowhere differentiable. proof Define$$\tag{34} \varphi(x) = \lvert x \rvert \... 1 vote 0 answers 65 views ### What is the Equation for the Batista-Costa Minimal Surface? The Batista-Costa surface is a triply periodic minimal surface. Three photos of part of the same surface are below: where the first two were taken form the research paper: The New Boundaries of 3D-... 11 votes 1 answer 254 views ### Beautiful errors in graph of$\sin(x^2+y^2)\$
I was writing a simple program to help visualize inequalities based on 2 variables. The test inequality that I was using was this: $$\sin\left(0.1(x^2+y^2)\right)\geq0$$ Regions that satisfy the ...