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Questions tagged [graphing-functions]

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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Finding the Shape of a Graph Using the Min and Max

QUESTION: Let $f(x)=2x^{2}-2x^{4}$. Find the open intervals on which $f$ is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). $f$ is increasing on the ...
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26 views

How to graph the motion of a projectile?

Suppose I have a projectile, fired at angle $\theta$, with velocity $v_0$, assuming it's only acted upon by gravity. How can I find an equation to enable me to plot the motion (vertical height against ...
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23 views

Help me finding function which give this type of graph.

Few days ago I was playing with graphing tool . For some function the graph came out to be like this- When I zoomed it where it begins,it gave graph like this- I was curious to know weather ...
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27 views

Sketching a region of a joint density function

This problem is from the textbook by John Rice, "Mathematical Statistics and Data Analysis": Let $X$ and $Y$ have the joint density function $f(x,y)=k(x-y),$ for $0\le y\le x\le 1$ and $0$ elsewhere ...
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How do we treat continuous variables inside summations?

I've been getting confused everytime we're graphing a summation with a continuous variable inside. For example, say I want to graph this equation with respect to $f$ ($y$ vertical, $f$ horizontal) $$ ...
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Changing this graph equation so it always passes through (1,1)?

I need a graph of $y=d*ln(cx+1)$ where $d$ is automatically calculated from $c$ so that it always passes through $(1,1)$. ie. Like this but where $d$ is calculated automatically from $c$: I tried ...
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Maxima — Drawing the feasable region of some inequations

I don't have much experience with Maxima but, I'd like to know how to plot the solution of a set of inequalities with two (or three) variables. It doesn't have to be Maxima, but any software I can ...
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39 views

How do I calculate the exponential regression with the following?

Not sure where to ask but I have a task to calculate the exponential function for curve fitting. So I have this exponential function: v(x)=a-(b*exp(-d*x)) I ...
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19 views

Appropriate number of significant figures to use in plot

I am trying to illustrate the convergence of a sequence of iterates by means of the following plot: convergence plot In my discussion I would like to state the fact that 1) the function is ...
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1answer
36 views

Using the floor function to define a periodic function

Is it possible to define the function defined in the following image using the floor function? If so, how? Update I tried your suggestion with Matlab's symbolic toolbox, ...
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122 views

Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices…

Let G = (V, E) be a simple undirected graph with n = |V | ≥ 1 vertices. A subset U ⊆ V of the vertices is called a vc-set if for every edge {i, j} ∈ E either i ∈ U or j ∈ U (or both). Let $U^∗$ be a ...
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How to convert values from one range to another with in-equal slopes and real time data?

There are two series , Sa and Sb. Sa ranges always within 0-1 . Sb ranges variably sometimes from 130-145, 2017-2077 and many more etc.. The data points are real time in nature. For each second ...
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21 views

Plotting a system of linear ODE

I would like to plot a system of following ODE: \begin{equation} \mathbf{\dot{x}} = \mathbf{Ax} \text{ where } \mathbf{A} = \begin{bmatrix} -2 & 1 \\ -1 & 0 \end{bmatrix} \end{...
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Sketching the region defined by a system

I have the following system: \begin{equation} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} xe^y \\ ye^x \end{bmatrix} \end{equation} which is enclosed in an area given ...
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25 views

How to draw the equation $x = r\cos(\theta)$ and $y = r\sin(\theta)$

Studying for calculus right now and in the notes it says a circle can have the equation x^2 + y^2 = r^2. ...
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24 views

How to express this simple equation in terms of a different variable?

I am using the equation: $$y=(1-e^{-ax})*d$$ For the shape of a logarithmic attack phase of an audio synthesizer envelope. The idea is for it to go from (0,0) to (t,1) at a given time (x=t) value. ...
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Create a multivariate function from a set of points

I am looking to construct a graph for illustrative purposes. I have a few restrictions that come from visualizing how the graph should look, in the form of $f(x,y) = z$. $f(\infty,\infty) = \infty$ $...
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How to draw a boxplot with whiskers correctly?

I want to draw a boxplot with whiskers where a lower bound is equal to $Q1 - 1.5 IQR$ and an upper bound is equal to $Q3 + 1.5 IQR$, where $Q1$ is a lower quantile, $Q3$ is an upper quantile and $IQR$ ...
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32 views

Why do only real roots intersect x axis for an equation?

If we draw graph of an equation with y = f(x) we see that x axis is intersected for only real roots of the equation. Y value can be zero for complex roots as well. Why then is this so? What is an ...
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24 views

How to plot the graph of this expression which involves dirac delta function?

I Was Doing a Problem on Electrostatics which required finding the charge density from the given electric field and then plot a graph of the charge density. I was able to find the charge density which ...
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What is the value of k if equation $x^3-3x^2+2=k$ has three real roots and if one real root?

I'd like help understanding this question graphically actually. My book finds the derivative of f(x)=$x^3-3x^2+2$ and gets 3x(x-2), thus finding maxima and minima of f(x) as 2 and -2. Then it just ...
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Changing the scale/span of y axis in a time domain plot

I have a set of x,y pairs, where x is always the time, and y can be anything, with any set ...
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2answers
21 views

When drawing function, compute $f',~f''$ first or vertical asymptotic first?

In Calculus, some functions don't have vertical asymptotics (e.g. $f(x)=2x+\cos x$), while some functions, say $f(x)=x+1/x$, may have vertical asymptotics. In the former case, we just compute $f'$ and ...
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Curve Represented by the Sum of Complex Moduli

I'm trying to integrate around a path defined below in the complex plane. I understand that if the region enclosed by the curve contains an isolated singularity then the value of the integral can be ...
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Estimate the degree of a curve given the graph

I am creating a program that, given an image of a graph, is able to estimate the function of the graph. In order to do so, some basic assumptions are made such as the graph follows the same behavior ...
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2answers
53 views

Understanding this graph

The function is given as $f(x)=2x+3x^\left(2/3\right)$. The enclosed graph is from wolfram.. My question is why doesn't $f(-1)=1$ show up to the left of the y axis. I don't see why the domain of ...
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1answer
24 views

How do you graph the derivative of an implicit equation?

For example, say you have y^2+5x=6x^3+4 Okay, so we do some implicit derivation and get 18x^2-5 / 2y Now... how is one to graph that? It is no longer y= or one function equaling another, it is now ...
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11 views

Simple data normalization for event visualization

I'm working on a dataset visualization and googling data normalization nowadays brings too much machine learning results. I'm looking for a strategy to normalize an unknown set of data between 0..1 to ...
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1answer
15 views

How to draw the function $f(x)=(x^2(e^x-1))^{\frac{1}{5}}$?

I would like to draw the following function: $f(x)=(x^2(e^x-1))^{\frac{1}{5}}$ I can draw the function $x^\frac{1}{5}$ pretty easily, but now I'm struggling to represent the function as a whole.
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Characterization of polynomials by their “shape”

Let me show how a general "shape" of a polynomial $P(x)$ of degree $n$ can be uniquely characterized by a sequence of small integers of length at most $n-3$. Let $\{ e_1,\dots,e_m \}$ be the extrema ...
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graphing exponential function

When graphing a function with exponentials in the numerator and denominator if you know its defined for all $x$ in $R$, can you do anything more than check the limits as it approaches positive and ...
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48 views

What may be this line's equation?

I have a line like this: The values are not perfect (means the values can be changed), but all are non-negative values. I like to know the equation's equation or function. I have tried- $y=\ln(x)$ ...
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1answer
25 views

How to find the function rule from a table?

I was trying to graph (1, 1)(2, 2)(3, 4)(4, 8)(5, 16)(6, 32)(7, 64)(8, 128)(9, 256)(10, 512) and I just couldn't do it. Does anyone know what the function rule of this is and how to find it in similar ...
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38 views

Creating a graph given condition of local minima and maxima

I had a question that goes like this: Let $m$ be the number of local minima and $M$ be the number of local maxima. Can you create a function where $M > m + 2$ ? Graph. I tried graphing it using ...
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1answer
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How does one find the intersection point between $y=(\sin x)^2$ and $y=\frac{2x}{\pi}$?

I was asked to find the points of intersection between $y=(\sin x)^2$ and $y=\frac{2x}{\pi} $ but I don't know how to go about it. Obviously they intersect at the origin. I also found out the other ...
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24 views

Constructing the graph from parametric equations

$$x(\theta)=|\cos4\theta|\cos\theta$$ $$y(\theta)=|\cos 4\theta|\sin\theta$$ $$0\le \theta\le2\pi$$ I have to graph the equation. Now, I have no idea as the parameter $\theta$ cannot be ...
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Graphical description of $g(x)=f(1/x)$?

I am working on a problem set out of Spivak's Calculus, and I am stuck on the following problem: Describe the graph of $g(x)$ in terms of the graph of $f(x)$. $$g(x)=f\left(\frac{1}{x}\right)$$ ...
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How do I find the equation for any given function?

If I am given a graph with labeled points, and I’m asked to find the equation that represents the given function, how can I do so? Just by looking at points it would be nearly impossible, and trying ...
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Plot and “meaning” of the function $ f(t, e^{At}\cdot x) = \left(1-\frac{1}{c\cdot r}\ \mathrm{dist}(x,B_r(0) ) \right)^+$

Fix $A \in \mathbb{R}^{m\times m}, c>0, r>0.$ Consider the function $f: \mathbb{R}_+ \times \mathbb{R}^m \to \mathbb{R}$ such that, for all $x \in B_r(0)$, it holds that $$f(t, e^{At}\cdot x) =...
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Plot in r with NA values

x=c(1,NA,3,8,4,8,NA) y=c(4,8,3,4,NA,7,6) plot(x,y, type="l") plot Plot does not connect the point(1,4) and (8,7). How can I do that?
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Find a continuous non polynomial function so that $\max|f(x)|=1$ for $0\leq x \leq 1$ and $\max|f(x)|$ is as big as we want for $1\leq x \leq 2$

I am asked to find a continuous, not polynomial function so that $\max|f(x)|=1$ for $0\leq x \leq 1$ and $\max|f(x)|$ is as big as we want for $1\leq x \leq 2$. I've come up with $$ f(x) = \left\...
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What would the 3D graph of GCD(x, y) and LCM(x, y) look like?

To find the answer out, I was going to use a graphing calculator but I couldn't find any one that supports the two operations. I would try to draw by hand but since it'll a 3D graph, I would have to ...
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Maxima or minima in a function [closed]

Suppose if a function is given which is differentiable throughout it's domain.This function has a line of symmetry say x=a, passing through the function.Then is it always true that the point at which ...
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1answer
36 views

Gaming AI, courage and retaliation

This is a bit oblique but maybe some of you will find it fun and it's been wrecking my brain for a while. Here's the background of what I'm trying to achieve, but if you want to skip to the actual ...
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How would you draw the graphs of the interactions between these functions?

I was wondering how I would draw the interactions between these functions if I were not given the equations for them (and am not allowed to make an equation). Please ignore my current drawings. ...
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1answer
25 views

How can I create a quadratic equation that flips the parabola, starting at a certain arbitrary point near the vertex?

Given an arbitrary quadratic polynomial $$ax^2+bx+c$$and a corresponding graph where gray lines are axis, black is the parabola, red is an arbitrary line near the vertex, How would you go about ...
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How to graphically add two functions

I have tried looking for tutorials or guides online, but I keep finding problems that are fairly similar but not exactly what I am looking for. I know how to add functions regularly, I am familiar ...
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$10000$ binary values get the frequency $1$ to $n$th

I have an exercise of probability I am trying to solve : We have a sequence of $10000$ equiprobable binary values and we write $f_n$ the frequency from $1$ up to the $n$th value. What is the sequence ...
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20 views

R plot graphics statistics people same birthday

I want to code the birthday problem in R using the plot . I've wrote the code the problem is that I get an error with that . Any idea is welcomed .Thank you very much . Edit edit I've changed the ...
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Which are differentiable for all x?

$F_1:$ \begin{cases} x^2/|x|, & \text{$x \neq 0$} \\ 0, & \text{$x=0$} \end{cases} $F_2$:$$|\sin(x)|^2$$ $F_3$:$$|\cos(x)|$$ I know that the absolute value of $\cos (x)$ would not be ...