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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How would you slove this graph transformation problem? [closed]

This is given the graph of y=f(x) enter image description here And the question is, what would this function look like based on the first function I mentioned enter image description here
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9 views

Graphic of Chebyshev net

I need to draw in latex the Chebyshev net of surfaces of revolution (Just for this example I don't need to have asymptotic curves, but if I facilitate the calculations it would be great). I have ...
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1answer
14 views

How to find the formulas for a "perfect-bell" curve between 0-1?

I would like to have a formula to generate the curves shown in the following plot: The magnitude of curvature should be adjusted by a parameter. Does there exist any well-known function or ...
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28 views

Non-decreasing function to a constant function

Let $f:[s,r] \rightarrow [0,q]$ be a non-decreasing positive function, where $s$, $r$, $q>0.$ Where $s$ is defined as the largest $t$ in $]0,r[$ s.t $f(t)=0.$ Suppose $\exists t \in ]s,r[$ such ...
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14 views

Fundamentals on creating a field equation [closed]

I am trying to brute force a novice grasp on field equations/graphs. Can someone provide me advice or insight on how would one actually approach a topic of creating an equation that describes a ...
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19 views

Need help finding examples of pairs of functions satisfying certain conditions

I want to find pairs of two functions on two variables $f_1(x,y)$ and $f_2(x,y)$, such that each one can be minimized on one variable ($f_1$ needs to have a minimum on the variable $x$ and $f_2$ needs ...
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1answer
40 views

Understanding the Graph of a Multinomial Distribution

I am trying to understand exactly what information the graph of a multinomial distribution is supposed to convey. The thing I find strange is that a binomial distribution is graphed in two dimensions ...
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1answer
34 views

How to derive a function for a circle intersection in polar coordinates?

There are two equal intersected circles (see picture below). I need to find a function, which describes the intersection area. I've tried to derive the function by modifying a cosine function, but it ...
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34 views

How do I derive the sinusoidal equation from this graph?

I don't understand how I can get the phase shift and period for this graph.
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3answers
82 views

The ellipse is known, but how to draw it?

Let the equation of an ellipse in general be given by: $$ Ax^2+Bxy+Cy^2+Dx+Ey+F=0 $$ Everything real valued, and well known it seems. But I have one question: how can we efficiently draw such an ...
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1answer
105 views

Why can't I graph $\sin(x)^{\cos(x)}$ in desmos? [closed]

My attempt at graphing; produced no results. This is what I get in Wolfram. What can I do to get it graphed in desmos?
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1answer
65 views

How to know if I have changed the graph of a function or not?

Case 1: $$\frac{2x^2}{4x^3}$$ $$\frac{1}{2x}$$ The graph hasn't changed. Case 2: $$\frac{6t^4+4t^2}{t}$$ $$6t^3+4t$$ The graph hasn't changed. Case 3: $$\frac{x^3-8}{x^2-4}$$ $$\frac{(x-2)(x^2+2x+4)}{(...
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1answer
40 views

How is a quantile-quantile plot different from a quantile plot? [closed]

I'm new to statistics so I don't know much. I'm not even sure how to properly ask this question.. But I would like to understand, how a quantile-quantile (qq) plot different from a quantile plot? Are ...
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24 views

odd first-order nonlinear ordinary differential equation [closed]

I have this equation $$y'[x]=\frac{y[x]^2+ A x - B y[x] x^m -C}{D y[x] x- E y[x]^2 x^m}$$ A, B, C, D, and E are constant but m we can choose. My first question is how to plot $Plot[y[x],x]$ this, and ...
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1answer
64 views

Does the order of graph transformations matter?

The task was worded this way: Suppose that $f(x) = \frac {1}{2}(x-1)^2 - 3$. State exactly how the graph of $y = f(x) $ will be transformed into: $ y = (3x-1)^2 +1 $ The answer I provided was: ...
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2answers
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Why does WolframAlpha give me an ugly graph for the input "(cos x-1)/x^2 when x=0.01"?

The function $\dfrac{\cos x-1}{x^2}$ is differentiable everywhere except for $x=0$. However, when I give WolframAlpha the input "(cos x-1)/x^2 when x=0.01", it gives me an ugly graph as ...
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2answers
61 views

How to find the coefficient a of a $y=ax^2$ parabola? [closed]

If you have a parabola mirror with a $y=ax^2$ graph in real life, how could you calculate the coefficient $a$? The only measurement that should be performed in real life is some kind of straight line. ...
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1answer
76 views

(simple) Why does the graph move to the left differently here?

I firstly graphed the following function: $$ y = (x)^2 $$ then I decided to graph the following function: $$ y = (x+4)^2 $$ As far as I remember from school course, here I have increased the h value (...
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2answers
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Based on the diagram of $f(x)$ draw the $g(x)$

Based on the diagram of $f(x)$ draw the $g(x)$? $f(x)$'s diagram : $g(x)= f(x/2 + 1)$ one solved it so: fist effected "$-1$" then "$*2$" to the "$x$" the other one ...
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0answers
30 views

Why is the $y$-intercept wrong?

I have a graph below where I put my data into an Excel sheet and try to obtain a linear equation for it using the trendline function. The equation that I obtained shows that the y-intercept is -105.09....
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1answer
42 views

Negative radial coordinates in polar plots

In polar plots $r=f(\theta)$, should a negative radial coordinate always be reflected? Even if $f(\theta+\pi)\neq-f(\theta)$? If $f$ does not involve any trigonometric functions? For instance, is this ...
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37 views

How to find the area of a changing geometric figure over time with MATLAB?

This problem seems simple, but is confusing to me. Assume we have a hollow tube with the cross section of circular cylinder that navigates with a constant speed through ice-covered waters. The outside ...
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3answers
100 views

While drawing graphs by hand, how correct is it to take unequal units on the x & y axes?

In exams and schoolwork, teachers allow us to take unequal units on the $x$ & $y$ axes if their values are really far apart for ease of drawing and scalability. For example, if the $x$ values are $...
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0answers
22 views

How to tackle growth rate order question?

How do I tackle these kind of growth rate questions? I almost always somehow rank them wrongly... Refer to screenshots: Q1 Q2 My current approach: I have a list of general orders: 1 < log n < ...
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1answer
63 views

periodic function of x with period 2 and f(x) =|x|−x for −1<x≤1.

Let $f(x)$ be a periodic function in $x$ with period 2, and $f(x) =|x|−x$ for $−1< x≤1$. Sketch the graph of the curve $y=f(x)$ in the interval $[−3,3]$. $f(x) =|x|−x$ seems not to be a periodic ...
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1answer
44 views

Find a function that satisfies...

I almost solve one problem, the thing is that to finish it I need to give an example of a function $f(x) \in C^1$ such that: $$ \int_{1/4}^1 (f'(x))^2 dx \leq \int_{0}^{1/4} (f'(x))^2 dx $$ and $$f(0)=...
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1answer
116 views

Why is $\frac{1}{\ln(0)} = 0$?

Why is $\frac{1}{\ln(0)} = 0$? I thought $ln(0)$ is undefined. The context is, I am looking for discontinuities in a function, and I expected $x=0$ to be a discontinuity since $ln(0)$ is undefined. ...
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30 views

Can anyone suggest a few good books based on Graphs and The Solutions of graphs

I just needed a few references of some good books for Graphs. I am looking for a book which just not only explain Graph Plotting but also to find the number of solutions of any type of equation be it ...
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2answers
75 views

Is $\ln(\sqrt{x^2 + 1} - x)$ an odd function?

$f(x)$ is an odd function if $f(-x) = -f(x)$. If $f(x) = \ln(\sqrt{x^2 + 1} - x)$, one can observe graphically that $f(-x) = -f(x)$. Hence, $f(x)$ must be an odd function. However, WolframAlpha gives ...
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0answers
29 views

Why is it that the graph of 2 equal functions differ as shown in the picture?

I was graphing $$y=\frac{x^{\frac{1}{3}}-4^{\frac13}}{x^2-8x+16}$$ and $$y=\frac{x^{\frac{1}{3}}-4^{\frac13}}{(x-4)^2}$$ but they seemed to differ at $x=4$ as shown in the picture. Why is that?
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43 views

A more elegant version of this spiral graph

The problem I set out to create a polar graph of a spiral with the following properties: (Listed in order of priority) It should be performant to calculate (A household computer should be able to ...
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28 views

Graphing rational expressions of trig/exp by hand?

In my math class, we are not allowed to use calculators. Thus, when I see problems with an exponent/log or trig either in top or bottom and I have to graph them to solve the problem, I'm not sure ...
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2answers
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How to graph modulus function graphs

I tried to find out a way to calculate the graph for multivariable modulus functions(eg. $|x|+|y|=1+x$) in this case made a table to find out all possible cases like: $y$/$x$ $x > 0$ $x < 0$ $...
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34 views

Plot a function as a function of another function in SageMath

I'd like to use Python's SageMath to plot a function as another function. In particular, I have two functions f(x) and g(x). I'd like to plot f(x) versus g(x). How can I do this?
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3answers
30 views

Writing the equation of a straight line parallel to the $y$-axis

I know that the general equation for a line is $y=mx+n$, where $m$ is the slope and $n$ is the value of $y$ when $x=0$. I was wondering how would you write the equation for a vertical line with the ...
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1answer
81 views

If a function $f$ is not defined on $[-2,0]$, what can we say about $\lim_{x\to-2}f(x)$?

I was thinking of a strange case in which we can say the limit is undefined. ( I mean different than the limit does not exist.) So I generated the graph of a piecewise function $f(x)$. There is a ...
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110 views

How Can I Visualize a PDE Boundary Condition?

In this question, the comment suggests that the integration bounds in the Fourier Series should be chosen to avoid discontinuities in the boundary conditions. I am trying to produce a nice visual to ...
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3answers
67 views

Approximate the graph of $e^{x^2}$

While solving the integrals related to $e^{x^2}$, we try to approximate it. My question is there some function of which the graph is approximately like that of $e^{x^2}$?
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1answer
36 views

Why does logarithmic scale give linearization here? [Low-pass-filter]

I'm given the formula for describing the voltage ratio bewerten in- and output for a low-pass filter (neglecting physical aspects): $\dfrac{U_{out}}{U_{in}} = \dfrac{1}{\sqrt{\left(\frac{f}{f_G}\right)...
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0answers
26 views

Are normal lines of a graph, tangent lines to another graph? And how can you induce it?

I was interested into normal lines of a curve, so tried to find out how many normal lines I can draw if I chose a random dot on the coordinate plane. The normal line trace of $y=x^2$ turned out like ...
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1answer
23 views

What do you call a plot where the increase/drop magnitude is equalized?

I've been looking at a COVID cases graph and realized that the normal growth/drop plot is actually misleading: In the middle of this plot we can see a peak growth rate of 56% and a peak drop rate of ...
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1answer
24 views

How can you determine where two polynomials cross and are tangent to each other, just by factorising the difference?

My textbook asked me to factorise the difference between P(x) and Q(x) and describe the intersection. I'm having trouble understanding: Why doing this would allow me to describe the intersection And ...
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2answers
36 views

The graph of a polynomial function of degree n is completely determined by any n + 1 points on the curve

Highschool maths student here, I'm having trouble understanding this statement: "The graph of a polynomial function of degree n is completely determined by any n + 1 points on the curve" Any ...
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2answers
282 views

Why is $n!$ so close to linear when plotted on a log scale?

I was considering the speed at which the factorial function grows, and thought to graph the function on a log scale. I noticed something interesting - it seems to approach a line. I graphed $f(x) = \...
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2answers
44 views

Why are the graphs of $y=\frac12\sin(2\sin^{-1}(x+1))$ and $2\sin^{-1}(x+1)=\sin^{-1}(2y)$ not the same?

Is there a valid reason why they are not the same? Because if you rearrange one equation then you get the other equation.
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1answer
36 views

How to deduce the function from the graph?

How to deduce the function from the graph? It is given that the degree of numerator of f(x) is 2 ** My Attempt** There are two asymptotes so the denominator should be in the form $k(x+2)(x-1)$. And I ...
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0answers
27 views

really simple doubt regarding minimum value of a super simple function

I don't have much to ask. Just wanted to know if it is actually possible to write out the minimum value of the function $f(x)=x^3$ whenever it is defined over $(1,10)$ (open interval). You can choose ...
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0answers
39 views

The graph of $y(x)=-x^2+bx+c$

The graph of $y(x)=-x^2+bx+c$ is shown below. Determine the signs (+ or -) of $b$ and $c$. $a=-1$ so the parabola opens downwards, but we can already see that from the given figure. How can we ...
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0answers
14 views

inflection points in composite function

I'm interested about how the inflection point in the original function result in the inflection points in a composite function. To approach that problem, I took a non-increasing cubic function f; $$f(...

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