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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Is breaks in the continuity of a graph scalar with regards to multiplying a constant?

I think I'm probably right but seeing how I've recently begun to go down the rabbit hole in mathematics that tends to produce all sorts of inconsistenties with any advanced conjectures that I make, I ...
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3answers
37 views

What is the function of provided dataset?

x | y 0 | 0 1 | 1 2 | 1 3 | 2 4 | 2 5 | 2 6 | 3 7 | 3 8 | 3 9 | 3 10 | 4 11 | 4 12 | 4 13 | 4 14 | 4 15 | 5 16 | 5 17 | 5 18 | 5 19 | 5 20 | 5 Desmos ...
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9 views

Inserting “holes” on a graph.

I am trying to plot the set $A = \big\{(x,y) \in \mathbb{R}^{2} \mid x^{2} + y^{2} < 2 \big\} - \big\{(0,\frac{1}{n}) \mid n=1,2,3 \dots \big\}$. I have tried different combinations of set ...
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0answers
16 views

Function for this 3D curve

thanks for your attention. I am trying to plot a 3D surface like the picture below to help depict the relationship between some variables. I have been fiddling with Google Search builtin plotter, ...
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1answer
51 views

How to analytically derive the geometric properties of a hyperbola and programatically use them to graph?

I have the following equation: $$ \left(10^{\left\lfloor\frac{\ln\sqrt k}{\ln10}\right\rfloor-1}+x\right) \left(10^{\left\lfloor\frac{\ln\sqrt k}{\ln10}\right\rfloor-1}+y\right) = k $$ Entering the ...
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41 views

Find an expression for the function which represents the bottom half of the parabola $x + (y-1)^2 = 0$

I can't seem to figure this question out. My workings are as follows: \begin{align*} x + (y-1)^2 & = 0\\ (y-1)^2 & = -x\\ y-1 & = \sqrt{-x}, \text{assuming that $x \leq 0$}\\ y & = ...
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1answer
37 views

Cis Graphs (Finding Values)

For this question: If you guys are not familiar with the $\operatorname{cis}$ notation $$ \operatorname{cis}(x) = (\cos(x) + i\sin(x)) $$ I've tried doing this: By comparing arguments $$ ...
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1answer
26 views

How would be the slope of $f(x)=y=ax$ where $x = \frac{a}{b}$?

Well, in physics we got $W = V\cdot I\cdot t \stackrel{R=^V/_I}{\Longrightarrow} \begin{cases} W = I^2\cdot R \cdot t \\ W = V^2\cdot \frac{1}{R}\cdot t \end{cases}$ In the first case the slope of ...
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1answer
47 views

X and Y intercepts

I have a function: $$y =\begin{cases} 3x, &\text{if } x ≠ 0; \\ 4, & \text{if } x = 0. \end{cases}$$ As I understand, function doesn't exist at (0;0). So, what ...
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1answer
44 views

Graphing of $y = (x^2 - a)^2$

I was graphing the equation $y = x^2 - a$ and I know why the graph is a parabola intersecting at the points $(-1,0)$ and $(1,0)$. However, when I graph $y = (x^2 - a)^2$, the graph oddly changes, as ...
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1answer
27 views

Combining two exponential distributions onto one graph

In a probability question I am working through, the question says the length of time of a football game, $s$ , is exponentially distributed with a mean of $\bar s$ . It then says to write out the ...
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2answers
46 views

piece wise function question

Let $$f(x) = \begin{cases} 0 & \text{if } x<0,\\ x & \text{if } 0\leq x \leq\\ 2-x & \text{if } 1< x \leq 2\\ 0 & \text{if } x>2 \end{cases}$$ and $$g(x) = \int_0^x ...
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1answer
31 views

equation from exponential graph

I am struggling to get an equation from the graph above I know ${f(x) = ba^x + c}$ When y = 0, x = -2 ${b = -2}$ ${24 = -2a^3}$ ${2a^3 = -24}$ ${a = {\sqrt[3]{{-24}\over 2}}}$
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1answer
26 views

Finding the equation of the line through X number of points?

I have a line graph with $8,000,000$ points. The X axis goes from $0$ to $7,999,999$ in increments of $1$ and the Y axis is either a $0$ or a $1$. There are no fractions on either axis. Is there an ...
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0answers
10 views

plot golden spiral along with rectangles showing the area split

I can see it's relatively simple to plot the golden spiral using the equation: $$r=e^{b\theta}$$ where $b={{ln(\varphi})\over{\pi\over2}}={{2ln({1+\sqrt5\over2}})\over{\pi}}=0.30634896253$ Here's ...
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2answers
28 views

Graph of a Function

Given $$ f(x) = \frac{1}{x – 2} + 5 \qquad x\neq 2 $$ Explain how the graph of $f$ can be obtained from the graph of $\frac1x$ by using appropriate translations. Include the image set of the ...
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0answers
33 views

How to Trace a Real-Life Flower Using Polar Equations?

Here is the flower I'm trying to trace: $\hskip2cm$ How can I trace this flower using polar equations? I currently have the formulas \begin{align} r_{1}&=1.75\sin(10\,\theta + 18) +3\\ ...
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3answers
47 views

Does every graph have an algebraic form?

Let's say I take a pencil and start drawing a curve on $xy$ plane. The curve is continuous and for each value of $x$ there is only one corresponding value of $y$. So question that interests me is - ...
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2answers
222 views

Integration of x^(1/2) sinx

My book say that integration of $x^{1/2} \sin x$ is not possible, why is it so? Which functions do not have an anti derivative? Does it mean that they do not have any area under the curve? But ...
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0answers
26 views

Graph Transformation

This question seems trivial to me but I still cannot figure out how to approach it. For any $x \gt 0$ and $f(x) \le 2^x$, how do I prove the following? $$ f(2x) \le f(x)^2 $$
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0answers
51 views

prove $x^{2n} + y^{2m} = 1$ is a “closed” shape

How do I show that $x^{2n} + y^{2m} = 1$ has a domain of $|x| \leq 1$? How would I show the opposite, that $$x^{2n-1} + y^{2m-1} = 1$$ has a domain covering all real values?
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Manual Graph Sketching For $\lfloor(x)\rfloor+\sqrt{x-\lfloor(x)\rfloor}$

How to prove $$\lfloor x\rfloor+\sqrt{x-\lfloor x \rfloor}$$ is continous for all $x$?And how to plot the nature of the graph manually? I can prove that at integer points it is continous.But what ...
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2answers
60 views

What is tangent to a curve or function?

When I read my textbooks or even type "what is a tangent?" on google, I have always got an answer similar to these lines: "A straight line or plane that touches a curve or curved surface at a point, ...
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0answers
12 views

How to graph polygon rising at an angle in 3D space from the origin of the coordinate axes with shaded region on the $x$-$y$ plane?

I am trying to obtain a graph just like this one that visually shows that an objective function is maximised in z-direction at a certain point and where the “ground” of the graph is the $x$-$y$ ...
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2answers
34 views

Functions and Graphs assumption of same algebra equation.

$$f(x) =\frac{ (x - 1) }{(x^2 - 1)}$$ $$g(x) = \frac{1}{(x + 1)}$$ Is $f = g$? why? Solution: answer is no. I don't get it. why can't it be same when it is the alt form?? Can anyone explain this ...
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1answer
28 views

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$ Hi, I've been working on a Simplex problem and would like to ...
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35 views

Why use ln-ln plot in proportional hazard test?

I recently study survival analysis since couple of months ago, and there is one question which makes me curious. a simple and (maybe) a stupid question. Why do we prefer to use ln-ln survival curve ...
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1answer
20 views

How can one determinate the variationt of $f(g(x))$

Given the two functions : $$f(x)=x^2-2x$$ $$g(x)=\sqrt{x+1}$$ The question is determinate the variation of $f(g(x))$ We have $D_{f(g(x))}=(-1,+\infty)$ For $f$ it's decreasing for $x<1$ ...
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2answers
35 views

Why is there $(2,3)$ corner coordinates on the graph, using this function: $f(x)=2x-1+|x-2|?$

Currently I am studying about absolute values and I had to consider this function and draw it's graph: $$f(x)=2x-1+|x-2|$$ I helped myself with symbolab, here is the link: ...
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3answers
74 views

Is there a solution for x for $x^2+(y-\sqrt[3]{x^2})^2=1$?

I tried to solve this equation (heart shaped function) for x, but cannot get a nice solution. Why? $x^2+(y-\sqrt[3]{x^2})^2=1$ The formula is taken from this image: I just wanted to rewrite the ...
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1answer
35 views

A scale for plotting zero to infinity

There are methods to convert quantities to certain scales and plot them on a graph (e.g., logarithmic scale graph). I wanted to plot quantities that belong to range $(0, \infty)$ on a graph of a fixed ...
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1answer
19 views

Parabolas ( making equation )

A parabola with vertex (1,5) has x-intercepts (a, 0) and (b, 0) where a<0, b>0, and 3 |a|=b . Find a·b. I tried making intercept form but it I can't do it. Please help.
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2answers
19 views

Graphing Parabolas ( finding area)

Find the area of the triangle formed by the origin and the points of intersection of parabolas $y=−3x^2+20$ and $y=x^2−16$. I tried graphing it. I could figure out what it meant when it's said formed ...
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0answers
43 views

subtracting a wave from a linear gives you a new type of wave, but what?

This is how I found out about it: This is a normal smoothing function, right? Both input and output go from 0 to 1 in a smooth function this is usually used instead of the normal x function, ...
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3answers
43 views

Given a diagram of $f(x)$, how do you find $f^{-1}(-1)$?

A question has a diagram of function f, with no function given (please ignore the purple line): If I wanted to find $f^{-1}(-1)$, would I draw the inverse of f along the x=y line and then find what ...
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2answers
32 views

is tg^-1 (x) not the same as tg(x)^-1?

Well, for better syntax, my question looks like this: Isn't $tg^{-1}(x)$ the same as $(tg(x))^{-1}$ ? I always thought that it was absolutely the same. But I was trying to solve a task on an ...
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2answers
16 views

potting of fractional exponential graph

Sir, please tell me how to draw the graph of $x^{1/2} + y^{1/2} = a^{1/2}$? I tried it many a times but couldn't find the solution. Please help me in solving the problem.
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1answer
43 views

How to display a graph with 5 variables?

I am working on a project and I need to display to my professor the following data involved with communication theory. I did an experiment varying distance(1/2/3/4 feet), delay amount between ...
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2answers
26 views

Graphing Parabolas Word Problem

A flying cannonball’s height is described by formula $y=−16t^2+300t$. Find the highest point of its trajectory. In how many seconds after the shot will cannonball be at the highest point? What is the ...
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1answer
26 views

Parabolas Inequalaties

If a vertical parabola opens upward, has its vertex in the third quadrant, and $y=ax^2+bx+c$ is the equation of this parabola, which of the following can be true? Sketch a curve for each possible ...
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1answer
31 views

Confusing solution to the limit of an implicit function?

$$\frac{8}{3}=\frac{\log{x}}{\log{y}}-\frac{\log{y}}{\log{x}}$$ When I graphed this implicit function on desmos (https://www.desmos.com/) it appeared as if there were two solutions as $x\to{0}$ from ...
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0answers
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Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.

Prove that the function $e^{-\sqrt{|\ln\text{frac}(x)|}}-(\text{frac}(x))^{\sqrt{\frac{1}{|\ln\text{frac}(x)|}}}$ is both even and odd function.Here $\text{frac}(x)$ is a fractional part function. ...
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2answers
31 views

Sinusoidal functions

I need to plot a graph of the following function for values time, $0≤t≤2π$ to $2π$ (radians). $$y=5\sin\left(2t+\frac{π}{6}\right)$$ I need to describe and define the amplitude, periodic time and ...
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2answers
30 views

A sinusoidal trigonometric function

I need to plot a graph of the following function for values time, $0\le t\le2\pi$ (radians). $$y=5\sin\left(2t + \frac\pi6\right)$$ I need to describe and define the amplitude, periodic time and ...
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0answers
16 views

Plotting of conics with variable eccentricity

The three types of conics (polar conic form, e.g., wiki) are plotted between a fixed focal point and a directrix line placed at a "fixed distance". Is it a two parameter plot? In what sense is she ...
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1answer
23 views

How to display character drawn by the Bezier curve

How can I draw/display a character based on Bezier equations? I have the plot equations: x(t)=3t-3t^2 y(t)=2-3t^2+2t^3 x(t)=3t-3t^2 y(t)=1-3t^2+2t^3 and ...
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0answers
24 views

Depicting a function which looks like a geometric sequence

I am to graph the following function: $f(x) = 1 + \frac{3x}{x^2 - 10} + (\frac{3x}{x^2 - 10})^2 + \dots $ I tried to use the formula for the sum of a geometric sequence, where: $a_0 = 1; m = ...
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1answer
36 views

Graphing a function of 4 variables

I have a function of 4 variables: i, r, s, and p. This is the function: $$f(i,r,s,p) = s*p(\frac{r} {1+i-r}) $$ D=$\mathbb{R}$ Is there a way for me to graph this function? Is it somehow possible ...
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0answers
25 views

Modified Bessel functions with negative argument

As recalled in a previous question, the modified Bessel functions of the first and second kind $I_{\nu}(x)$ and $K_{\nu}(x)$ can be obtained from $J_{\nu}(ix)$ and $N_{\nu}(ix)$: that are the Bessel ...
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2answers
41 views

Prove that if a particle travels a unit of distance in one unit of time starting and finishing in repose it has in a moment an acceleration $\ge 4$

How would you solve this problem? Prove that if a particle travels a unit of distance in one unit of time starting and ending whith velocity $0$ it has in a moment an acceleration $\ge 4$ (positive ...