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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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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275 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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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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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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68 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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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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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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30 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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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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36 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
81 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
47 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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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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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
47 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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33 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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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
61 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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32 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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28 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
38 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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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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33 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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32 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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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
32 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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26 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
115 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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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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42 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 ...
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149 views

Jigsaw Equation

I'm looking for an equation that looks like the image below. I am comfortable constructing functions that pass the vertical line test, but as this is a relation, I am not really sure how to start. ...
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9 views

A Supply Curve in Negative Axis

I am plotting a MACC curve, but the main issue is that the ranking it gives is wrong when the cost effectiveness are negative. In particular, the curve plots dollar/kg against kg as a means to rank ...
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1answer
24 views

is there an easy way to find the inflection point of this function?

From a past exam. For the function y=x(x-3)^2/5, is there trick to find the inflection point? Doing the second derivative takes a while and gives messy results, and the space they give me to work out ...
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1answer
18 views

Help with graphing an exponential function

I know this is probably a very easy question, but how do you know the difference between an exponential that is decaying at an increasing or decreasing rate? I multiplied $e^{i2\omega}$ by a box and ...
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Which of the following equations have the same graphs? $(A)y=x-2\,(B)y=\frac{x^2-4}{x+2}\,(C)(x+2)y=x^2-4$

Which of the following equations have the same graphs? $1.y=x-2\hspace{1cm}2.y=\frac{x^2-4}{x+2}\hspace{1cm}3.(x+2)y=x^2-4$ I know that the graph of first and the second functions are different ...
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1answer
31 views

Plotting a function around $0$ shows it is jumping around, although the limit as $x\to 0$ exists

My problem revolves around the function: $$ f(x) = \frac{\sin(\tan x) - \tan(\sin x)} {\arcsin(\arctan x) - \arctan(\arcsin x)} $$ The $\lim_{x\to 0}f(x)= 1$. However, whilst approaching 0, there is ...
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Sketching the graph of a fourth degree polynomial curve

My approach doesn't seem to work. $$(y^2-2)^2+(x^2-2)^2=2.$$ Any suggestions and solutions would be appreciated .
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How to create a set of equations using coordinates

We were tasked to graph an object for our project. We plot the eggplant on a cartesian plane and have coordinates for it The catch is we need to make different combinations of equations to connect ...
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1answer
25 views

Inequality problem for graph and straight line intersection

I have having trouble to solve a revised-GRE graph math where it is very essential to find the answer with shortest amount of time. The way I wanted to solve this math is, to find the ...
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1answer
25 views

How to sketch a graph given a function and nothing else?

First, apologies about the basic question, I'm a first time Calc I student with no prior calc experience. I'm looking for the general steps of how to sketch a graph given a basic function like ...
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11 views

Graph Sketching and Transformations

Sketch the following $$y = f(x)$$ $$y^2 = f(x)$$ $$y = f(x^2)$$ $$y^2 = f(x^2)$$ Obviously you can't sketch these, but how does each graph differ from the first one, i.e. how are they transformed ...
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2answers
67 views

What does $f(x,y) = x + y$ mean in graphing?

All right, so I'm supposed to graph these $5$ things: $$x \geq 3\\ x\leq 6\\ y \geq 3\\ y \leq 6\\ f(x,y) = x + y$$ I was able to graph the first four, but I have no idea what the last one means. I ...
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25 views

Is there free software to graph (draw) a time series plot over a period of time that I specify?

I have some data measured at 15 minute intervals. For a presentation, I'd like to plot (animate?) the data over the course of 30 seconds or so, so that the audience can have a sense of the changes at ...
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graphing of two realtions

We have the following relations: $$S_1=\{(x,y) \in Z^2:x+y>1 \text{ and } x>0 \}$$ $$S_2=\{(x,y) \in P^2:x+y>1 \text{ and } x>0 \}$$ We have to make the graph for each occasion. My ...
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1answer
12 views

What PC programs or iPad applications are there which allow you to plot cylindrical/spherical polar graphs?

I've been trying to get my head around the use of cylindrical and spherical polars to plot graphs. I feel that the easiest way to do this would be to try plotting some, but I'm struggling to find a ...
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31 views

Cumulative return, portfolio performance

I calculated the daily returns for 10 decile portfolios. Now I would like to make a diagram where the cumulative performance is shown or in other words the performance of the portfolio through the ...
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2answers
49 views

Sketching $y=a^x-a^{2x}, a>0$

When I need to sketch: $y=a^x-a^{2x}, a>0$, do I need to graph two functions? One when $0<a<1$ and the other when $a>1$? I didn't get any difference in the ascending descending ...