Tagged Questions

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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Horizontal Asymptotes

Find all asymptotes of: $$f(x) = \frac{a + be^x}{ae^x+b}$$ The way I've been taught is that the $+a$ and $+b$ in the numerator and denominator respectively do not contribute when x tends to infinity,...
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Name this 2-dim Parametric Curve

is there a name for the following parametric curve? Thanks. I encountered it when playing around with the tangent lines and normal lines of an ellipse. The parameter $\theta$ is the same parametric ...
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Behaviour of the solution of an equations as a function of a parameter

Let $x$ be the smallest positive solution of the following equation $$x=\frac{1}{\beta}\ln x+a-\frac{1}{\beta}\ln a+c$$ where $\beta>1$ and $a,c\in(0,1)$ are fixed constants. I need to know the ...
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Are polynomial fractions and their reductions really equal? [duplicate]

I'm reading Larson's AP Calculus textbook and in the section on limits (1.3) it suggests finding functions that "agree at all but one point" in order to evaluate limits analytically. For example, ...
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How to get the output of a signal given the input and impulse

Here is my question So given the input and impulse response how would I go about getting the output? The output is given in solution (in teal) but I have no idea how to get it . thanks
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What direction should the graph be?

Graph the function $f(x) = \dfrac{x^2+2x}{x^2-4x+3}$, labelling all intercepts and asymptotes. I found the vertical and horizonal assymptotes myself.I plugged the problem into an online graph ...
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Is an annulus with its outer circle excluded (< instead of ≤) considered bounded?

I have the function with its domain defined by x^2+y^2<25 and x^2+y^2≥9. This gives me an annulus, with the inner circle centered at the origin with radius 3 and the outer circle centered at the ...
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Solve for and Plot the Relationship Between Mean and Standard Deviation of a Normal Distribution Conditional on Satisfaction of A System of Equations

I am trying to use Mathematica, R, or Matlab to solve for (since it cannot seem to be solved analytically) and plot the relationship between mean and standard deviation of a normal distribution ...
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I'm having trouble understanding what this problem is asking me

This is the problem So my problem is that I dont know how to solve it... I have learned about system of inequalities and that kinda stuff, but I never got anything like this. I do not want anyone to ...
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How to make a graphic of this problem? [on hold]

I've got 4 parameters which are independent one from another, like $A,B,C,D$, the range of the parameters is $[0,1]\in \mathbb{R}$. Each one of them are a property of an object $\phi_k$. I've got 16 ...
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Why is the graph incomplete?

I've put this formula in google: log(2x-3) And it draws this graph: link to graph Why is the graph not being drawn all the way down? It is supposed to follow the ...
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How to visualize change over time of multiple items at once?

I'm writing a recommendation system for a news website. At any point in time, there are between 50-100 articles that are candidates for recommendation based on the algorithm, etc. What I'm trying to ...
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Correct Order of Applying Graphical Transformation with Absolute Value

I was going through this website, reading about transformations of graph when $| |$ is applied to various parts of a given function, $y=f(x)$. Going through the fourth example of the page, I came ...
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How to graph hypocycloid on graphical calculator

I want to know how I can graph a hypocycloid using my TI-nspire calculator. I already know the parametric equations for hypocycloids which is: Parametric Equations of Hypocycloids Does anyone know ...
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Absolute Value Graph Problem in Gelfand's Functions and Graphs

I am working through Gelfand's Functions and Graphs, where I am currently on the absolute value section. At the end of the chapter practice problems, Gelfand poses a set of problems regarding ...
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Unable to comprehend results of principal component analysis

(Image below) Image shows the principal component analysis of two points {(1,3), (3,1)}. u1 and u2 are drawn which are corresponding eigenvectors after PCA. The points follow a normal distribution N(0,...
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How do I add chart points together? [closed]

In this video, two points on a chart are added together. As each individual point has X and Y values, how is addition performed? I've researched 'adding chart points' and variations thereof but not ...
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How to graph a level set of $f(x,y)=\sqrt{4-x^2-y^2}$?

If the definitions are: $$D=\{(x,y) \in\mathbb{R}^2 \mid x^2+y^2<4\}$$ $$f:D\rightarrow\mathbb{R}$$ $$f(x,y)=\sqrt{4-x^2-y^2}$$ How do I graph the contour line (subset of $D$) where $f(x,y)=c$ ...
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Reading a 3d graph to generate a 2d projection.

I know this will sound very dum but I have spent some good time trying to understand before posting this question. Basically, I need some help in understanding how (a) and (b) are being used to ...
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How to find f(23) given part of the graph and that f(x)=f(x+6)? [closed]

I am very confused, how can $f(x+6) = f(x)$ for all $x$ since $f(x+6)$ would be a shift version of $f(x)$, unless it is a straight line? is the answer D? $6+6+6+6 =24$ $\Rightarrow$ $f(23) = f(5) = 4$...
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Why do graphing calculators plot this function wrong? Wolfram Mathematica example.

Wrong graph of the function f(x)=-1^x The function in question is $f(x)=-1^x$ and the plot example is from Wolfram Mathematica. The graph is supposed to show a zig-zag otherwise known as the triangle ...
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I am skeptical of my results (percent rate of change)

Excuse the png equations, still a MathJax newbie. I am analyzing data I have computed: Alcohol content and Caffeine content retention after a duration of 8 hours for each. I had gotten the data in ...
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Why do non-linear functions have to be in V or U shape, why can't it just be one line? [closed]

The title says it all really, I just don't get why you can't just use one line.
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What would be the graph of absolute value of $X - Y$

I am solving a question, where I need to find the expected value of the absolute value of $X-Y$ where $X$ and $Y$ are two independent uniformly distributed random variable. So I was looking for the ...
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If $f(x)=x^3-3x^2-x+2$ ,Find an expression for the function $y$, which is obtained by rotating the graph of $f (x)$ through $180°$.

Question: $f(x)=x^3-3x^2-x+2$ where $x\leq 1$ Find an expression for the function $y = g(x)$, where $x\geq1$ , which is obtained by rotating the graph of $y = f (x)$ through $180°$ about ...
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Graphs of the hours of daylight in certain latitudes

Problem Attempt We are given that Graph A is North. Since South is more "dark" when North more "light" I picked the graph that is mirrored horizontally: Graph D. For East and West I can only ...
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Approximate a function from points

I would like to approximate a polynomial equation from a series of points. Searching around this site I found this post which pointed to the Lagrange Interpolating Polynomial. The challenge however ...
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Is a sigmoid function what I need to make this graph?

I'm designing a game where characters' speed starts slowing down after different distances. I'm not advanced in mathematics so I'm not sure if I'm on the right track. After researching on wikipedia I ...
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If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$

If $f(x,y)$ is a function that its contour lines are straight, is it necessary looks like $f(x,y) = ax + by + c$? Well, in the answer is no. it is written that $e^{x+y}$ for every $(x,y)$ has ...
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Graphing $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$: help please!

I am investigating the sequence that tends to the limit $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$, and although I am making headway on related theory, I would like to graph the ...
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Transforming a set of scatter points

I have a set of prediction scatter data y vs x in black crosses below. For the prediction to be 'accurate', the points ought to fall on the 1:1 line. I am trying to quantify a correction scheme to ...
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Testing for symmetry about a curve/line

In High School Algebra , after studying how to plot a graph of $f(x)$ (rather called $y$) against $x$ in Cartesian coordinates, we studied several tests to determine the symmetry of the plotted graphs ...
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$\tan x= \cot (x+\phi)$ for some $\phi$

Suppose we graphed the equation $y = \tan x$. Is it possible to describe this graph with an equation of the form $y = \cot (x + \phi)$, for some number $\phi$? Why or why not?
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For what values does $kx^2 - 6x - 4 = 0$ cut the x-axis? [closed]

A quadratic equation problem. For what values does $kx^2 - 6x - 4 = 0$ cut the x-axis? The preceding part of this question dealt with the discriminant.
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Finding Intermediate points in a graph

I have the following values in a table,I would like to find the intermediate points(Need to find y values for example if x=33 then the Y value for that x value) between the given values.But I could ...
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y-axis dynamic domain padding to center graph

I'd like to know how to add extra numbers on a graph's y-axis? Aside from the values shown in the image, this axis can be thousands and even millions. I'm trying to center the lines so the min (-30) ...
Plotting $\sum_{n\geq 1}\frac{1}{n}z^{n}$ for $|z|<1$ (the natural boundary): Coding
As part of my tutorial, I would like to show the plots of a)$-\sum_{n\geq 1}\frac{1}{n}z^{n}$ and b)$Log(1-z)=log(|z|)+iArg(z)$, to drive home the point of analytic continuation. Plotting the Log is ...