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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1answer
13 views

Shape of a functional curve [closed]

Can someone help me understand the shape and visual of the following functions: z = 36xy + 6( y - x ) - 1.
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1answer
56 views

How to sketch $\cos (xy)$ by hand

I've been practicing sketching maps $\mathbb R^2 \to \mathbb R$ and mostly I can do it but this one has me stuck completely. I want to sketch $\cos (xy)$ by hand. Here is what I have so far: For $...
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1answer
30 views

Does cancellation impact vertical asymptotes?

Question: Let $r(x) = \frac{(x^2 + x)}{(x + 1)(2x - 4)}$. Does the graph has $x = 1$ as one of its asymptotes? Answer: No. My reasoning: $\frac{(x^2 + x)}{(x + 1)(2x - 4)} = \frac{x(x + 1)}{(x + 1)(...
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1answer
31 views

Finding a function with a certain behavior

I'm searching what are the keywords or the good links to expand my researches. I would like to get the equation ( for programming purposes ) of more or less this curve: http://i.stack.imgur.com/...
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2answers
31 views

parametric polar equation of a circle

I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$. I am attempting to convert the generic equation for a ...
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4answers
63 views

Graphing $\frac{(x-3)}{(x^2-3x)}$ and $1/x$

For graphing the first equation, in the solved example given in the textbook, we proceeded as follows: $\frac{(x-3)}{x^2-3x} \implies \frac{(x-3)}{x(x-3)} \implies \frac{1}{x}$ for $x \neq 3$. Now ...
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4answers
33 views

How to shift a line in a graph regardless of slope?

I want to shift a line right some points, regardless of its slope. For example, a vertical line will shift to the right by having its two y coordinates changed, [(x1, y1+some number) (x2, y2+some ...
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1answer
33 views

Hi I was wondering if there is any algebraic way to find the zeroes of a cos/sin formula without using the unit circle? [closed]

I understand how to find the zeroes using the unit circle or just graphing it for any matter for my equation. I was just wondering if there is a formula or an algebraic way I could find them. Here'...
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4answers
44 views

How to understand $|1+z|<1$ where $z\in\mathbb{C}$ geometrically?

I am trying to understand how to plot $|1+z|<1$ where $z\in\mathbb{C}$, is it a circle centred at real axis $\text{Re}(z)=-1$ with radius $1$? My question is how can we show it algebraically? I ...
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0answers
27 views

Discontinous and differentiable

If we have a two functions $f:[-1/2, 2] \to \mathbb{R}$ $g: [-1/2,2] \to \mathbb{R}$ $f(x) = [x^2-3]$ where $[ \cdot ]$ denotes greatest integer $g(x) = |x| f(x) + |4x-7| f(x)$ Now we have to ...
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2answers
23 views

Number of solutions using graph

We have to find the number of solutions of $e^((-x^(2))/2)$ + $-x^2 =0$ I tried it and got one solutions by drawing graph. Is I have done correct ? My try is on :
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0answers
21 views

Is there a mathematical term for the “de-peaking” of a dataset

I have several sets of data that exhibit similar "peaks" when viewed as a graph, e.g.: A more useful representation of this data (for my purposes) is ${y = abs(x - 70)}$. The representation of the ...
4
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1answer
49 views

Graphically solving for complex roots — how to visualize?

So recently we've been doing the complex roots of quadratics, cubics and polynomials in general in school. But my question is, is there a way to see where these roots are, just like you can see where ...
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2answers
69 views

What does the graph of $\sin^2 x$ look like?

When solving trig equations, sometimes it comes out as a hidden quadratic, like this: $2\sin^2x-5\sin x+2=0$ Obviously it is possible to factorise and solve for $\sin x$. I understand graph ...
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1answer
25 views

Describing the set of all points

Is there a way to describe the set of all real points in a single equation with an equals sign? Instead, is it possible to create a "function" (I use function loosely as it mathematically is supposed ...
1
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1answer
27 views

Finding the points of intersection

Let f(x) be a real valued function defined for all real numbers s such that $|f(x)-f(y)| \leq (1/2)|x-y|$ for all $x,y$. Then what is the number of points of intersection of the graph of $y = f(x)$ ...
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0answers
23 views

forbidden chromatic polynomial

We wish to show below chromatic polynomial are not exist; It means that we couldn't find any graph that has one of these chromatic polynomial 1- $\ k^5 - 4k^4 + 8k^3 - 4k^2 +k$ 2- $\ k^4 - 3k^3 + k^...
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1answer
17 views

MuPAD: plot sum of list elements

I am receiving an unclear error when trying to plot partial sums of elements of a list in MuPAD. Any suggestions would be appreciated. ...
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0answers
6 views

Mupad Scatterplot operand is invalid

Could someone please explain the following error? I am trying to plot (0,0) and (1,1) on a scatterplot in mupad. ...
2
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3answers
25 views

How to draw the graph of the optimised function in linear programming

Ok, I don't know if I am just over thinking this, but I have been tearing my hair out trying to think about this. I have looked at plenty of linear programming examples and solutions online and I can'...
2
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1answer
65 views

How to graph $\frac{(x+3)}{(x+1)}$?

I'm not looking for plotting values. I mean something which can be done without it. For example, for the function $f(x) = mx + b$, we can use the slope $m$ and the y-intercept $b$ to easily graph the ...
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3answers
53 views

What is the logic behind the method used to shift a graph horizontally? [duplicate]

I understand why we add or subtract from $f(x)$ to move the graph vertically. To move it up, we move all the values up by adding whatever constant value we want. However, when it comes to horizontal ...
2
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2answers
62 views

Sketch the heart and indicate its orientation with arrows $ r = 1 - \cos(\theta)$. Find the area enclosed by the heart

Hi all I am trying to figure out how to sketch the heart. Here is what I have tried so far: $$r = 1 - \cos(\theta) \\ r(r = 1 - \cos(\theta)) \\ r^2 = r - r\cos(\theta) \\ $$ Use the fact that $$r =\...
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0answers
19 views

Function for asymmetrical pyramid with a rectangular base

I would like to derive a single function for a pyramid (corners can be rounded) that has it's tip always centered on x=0,y=0 and the size and position of the base - dynamic, depending on the variables....
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1answer
48 views

A graph G which can’t be painted properly in 2000 colors

A graph G which can’t be painted properly in 2000 colors (i.e. any two adjacent vertices have different colors) is given. The graph is properly painted in 2016 colors. Prove that a path of length 2000 ...
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0answers
30 views

Graphing complex numbers on Casio fx-9750 GII

I have a Casio fx-9750GII, I'm starting to get to grips with just how useful it can be. For those familiar with it you will be aware it can graph functions. However I noticed when looking through the ...
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2answers
42 views

Given the equation of a line, travel X points along it.

I have the equation of a line: $$y=\frac{7}{4}x\ +\frac{9}{2}$$ I want to find the point 4 units along the line, starting from the point $(-2,1)$. I tried using Pythagoras and forming this equation:...
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1answer
29 views

Does $f(x) = \frac {1}{(tanx)^2}$ has any x-intercepts?

I want to draw the following function $$f(x) = \frac {1}{(tanx)^2}$$ My intuition tells me that it does not have any x-intercepts because the numerator will never equal to zero but the online grapher ...
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0answers
16 views

Graph method for representing multiplicity of solutions

Inspired by Degenerate zeroes Fundamental theorem of Algebra In Cartesian coordinates if a root has a multiplicity of even then it "bounces" back up from the $x$-axis, if the root has a multiplicity ...
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1answer
28 views

Find set of values for $k$ with two distinct roots?

Find the set of values for $k$ for which the line $y=2x-k$ meets the curve $y=x^2+kx-2$ at two distinct points. I have started my equation like this: $$x^2+kx-2=2x-k$$ but I need to put it in the ...
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0answers
19 views

Good way to plot coordinate system in computer?

I want to plot a coordinate system rotation in my paper, I want to know what would be a good way to make the plot? The plot would look like:
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1answer
48 views

Counting Turns in a Rectilinear Spiral Graph

So consider a rectangular spiral graph which starts at the origin, goes right 1, up 1, left 2, down 2, right 3, ... (in units). How can we tell how many turns there have been given a point? For ...
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1answer
14 views

forming log equation from graph points

Okay so I need to form a logarithmic equation from the points (1960,4.7) (1964,5.1) (1968,5.4). I have 'guess and checked' to get the equation 2.7421 log(x-1950)+1.9579, and was wondering if there was ...
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0answers
21 views

How can we find roots of ${x_\mu }=2\mu$?

Let ${c_m}{x^m} + \cdots + {c_1}x - \mu = 0$ where $\mu \in (0,1)$ and ${c_1}, \ldots ,{c_m} > 0$. Suppose ${x_\mu }$ be positive root of this equation. How can we find roots of ${x_\mu }=2\...
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1answer
45 views

Finding Solutions (with only pen and paper)

For what least value of $k$ does the equation:$$e^x=kx^2$$ Have 3 solutions? Let $f(x)=e^x$ and $g(x)=kx^2$. For a positive $k$, drawing a rough graph of $f(x)$ and $g(x)$ does show 2 solutions of ...
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3answers
80 views

Why Can't I graph $(-1)^x$?

I tried to graph $(-1)^x$ but got nothing. Then I went on and tried $(-1)^{3.2}$ and got -1 as the answer, but when I tried $x=3.3$ instead I got an error. I know that when x is a natural number that ...
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0answers
9 views

Graph and Stitch Piecewise Function

I am trying to develop a model to describe the rate of something increasing. It increases 88983 for 1.26s, then stops for 2.3s. It repeats this cycle indefinitely. The best I could come up with is: ...
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0answers
7 views

Let G be bipartite on n vertices

Let G be bipartite on n vertices .Prove that $\alpha=\frac{n}{2} $ if and only if G has perfect matching.. Suppose $X\subseteq A$ and $|X|\gt n/2$ Then every vertex in B must be adjacent to a vertex ...
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0answers
20 views

Geometric interpretation of the nth root of a quaternion?

For ordinary imaginary numbers, $(r,\theta)$ turns into $(\sqrt{r}, \theta /2)$ for the square root and it is similar for higher roots. Is there an analogous interpretation for roots of a quaternion?
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0answers
14 views

How to change position of the axes values of a Sage plot.

I am plotting 2D functions on Sage, and I would like to move the values displayed along the $y$ axis (the ticks) from the left of the axis to the rigth, because they bother me there. I had a look and ...
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1answer
14 views

Drawing $D=\{(x,y)| |x-1|+|y-1|\leq \frac{1}{2}\}$ in $\mathbb R^2$

$$D=\{(x,y)| |x-1|+|y-1|\leq \frac{1}{2}\}$$ I know how $y=|x-1|$ looks, and $|y-1|$ but how do I find this? The problem I have is to find $$\iint_{D}|\ln(xy)|dxdy$$. I think I can do this, just need ...
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0answers
8 views

Plot a graph with two inputs and two result

I want to plot a graph with two inputs, transmission rate and scan perido, and the result will also be two results, time of detection and number of detected packets. Shall I use two graphs to plot ...
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2answers
31 views

Based on the function graph, in how many points the derivative equals 2?

I need to answer the question in the title for this function graph. [] I see that the derivative is positive in $3$ segments of the graph, and thinking about it as roughly $\frac{\bigtriangleup y} ...
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0answers
18 views

Suggestions for plotting data and representing it on a table

I've never been good with graphs so reading up some graphing tips didn't really give me the answers I was looking for. I'm planning to plot some data into a line / scatter graph and unsure how to ...
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3answers
19 views

Sketching the graph of trigonometric functions involving absolute value function

How do I sketch the graph of $\tan |x|?$ I know that the modulus over $|x|$ can be thought of as the angle (in radians) will always be positive which implies that the angle is always measured anti-...
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1answer
42 views

Ratios within sine graph

Line $AB$ goes from the origin $(0,0)$ to the maximum point of the sine graph at $(90,1)$. Line CD is perpendicular to line $AB$ and is at the point at which the distance along this line between line $...
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1answer
19 views

Defining composite of piecewise function

Let $$f(x) = \begin{cases} x+2, -3\leq x \lt-1 \\ x-1,-1\leq x \lt3 \end{cases}$$ I had to find $f(f(x)$ I defined $f(f(x)$ to be: $$f(f(x)) = \begin{cases} f(x)+2, -3\leq f(x) \lt-1 \\ f(x)-1,-1\...
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3answers
31 views

how to know spot a repeated root in a graph

The diagram shows a cubic curve passing through (–1, 0), (2, 0) and (0, –8). What is the equation of the curve. So I would have said: $-8 = k(x + 1)(x-2)$ $k = 4$ $y = 4(x+1)(x-2)$ but the root ...
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1answer
20 views

Equations of Custom Curves

How would one find a equation or a function to describe a custom curve in a coordinate system? Like for example, when someone presents you with a graph of a repeating curve, how would one find its ...