# Tagged Questions

Questions regarding the plotting or graphing of functions. Questions about graphs with vertices and edges should use the (graph-theory) tag instead.

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- $\ k^4 - 3k^3 + k^... 1answer 27 views ### MuPAD: plot sum of list elements I am receiving an unclear error when trying to plot partial sums of elements of a list in MuPAD. Any suggestions would be appreciated. ... 0answers 7 views ### Mupad Scatterplot operand is invalid Could someone please explain the following error? I am trying to plot (0,0) and (1,1) on a scatterplot in mupad. ... 3answers 26 views ### How to draw the graph of the optimised function in linear programming Ok, I don't know if I am just over thinking this, but I have been tearing my hair out trying to think about this. I have looked at plenty of linear programming examples and solutions online and I can'... 1answer 66 views ### How to graph$\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$to easily graph the ... 3answers 57 views ### What is the logic behind the method used to shift a graph horizontally? [duplicate] I understand why we add or subtract from$f(x)$to move the graph vertically. To move it up, we move all the values up by adding whatever constant value we want. However, when it comes to horizontal ... 2answers 64 views ### Sketch the heart and indicate its orientation with arrows$ 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 $$r =\... 0answers 19 views ### Function for asymmetrical pyramid with a rectangular base I would like to derive a single function for a pyramid (corners can be rounded) that has it's tip always centered on x=0,y=0 and the size and position of the base - dynamic, depending on the variables.... 1answer 48 views ### A graph G which can’t be painted properly in 2000 colors A graph G which can’t be painted properly in 2000 colors (i.e. any two adjacent vertices have different colors) is given. The graph is properly painted in 2016 colors. Prove that a path of length 2000 ... 0answers 37 views ### Graphing complex numbers on Casio fx-9750 GII I have a Casio fx-9750GII, I'm starting to get to grips with just how useful it can be. For those familiar with it you will be aware it can graph functions. However I noticed when looking through the ... 2answers 42 views ### Given the equation of a line, travel X points along it. I have the equation of a line:$$y=\frac{7}{4}x\ +\frac{9}{2}$$I want to find the point 4 units along the line, starting from the point (-2,1). I tried using Pythagoras and forming this equation:... 1answer 29 views ### Does f(x) = \frac {1}{(tanx)^2} has any x-intercepts? I want to draw the following function$$f(x) = \frac {1}{(tanx)^2}$$My intuition tells me that it does not have any x-intercepts because the numerator will never equal to zero but the online grapher ... 0answers 16 views ### Graph method for representing multiplicity of solutions Inspired by Degenerate zeroes Fundamental theorem of Algebra In Cartesian coordinates if a root has a multiplicity of even then it "bounces" back up from the x-axis, if the root has a multiplicity ... 1answer 28 views ### Find set of values for k with two distinct roots? Find the set of values for k for which the line y=2x-k meets the curve y=x^2+kx-2 at two distinct points. I have started my equation like this:$$x^2+kx-2=2x-k$$but I need to put it in the ... 0answers 19 views ### Good way to plot coordinate system in computer? I want to plot a coordinate system rotation in my paper, I want to know what would be a good way to make the plot? The plot would look like: 1answer 50 views ### Counting Turns in a Rectilinear Spiral Graph So consider a rectangular spiral graph which starts at the origin, goes right 1, up 1, left 2, down 2, right 3, ... (in units). How can we tell how many turns there have been given a point? For ... 1answer 14 views ### forming log equation from graph points Okay so I need to form a logarithmic equation from the points (1960,4.7) (1964,5.1) (1968,5.4). I have 'guess and checked' to get the equation 2.7421 log(x-1950)+1.9579, and was wondering if there was ... 0answers 21 views ### How can we find roots of {x_\mu }=2\mu? Let {c_m}{x^m} + \cdots + {c_1}x - \mu = 0 where \mu \in (0,1) and {c_1}, \ldots ,{c_m} > 0. Suppose {x_\mu } be positive root of this equation. How can we find roots of {x_\mu }=2\... 1answer 46 views ### Finding Solutions (with only pen and paper) For what least value of k does the equation:$$e^x=kx^2$$Have 3 solutions? Let f(x)=e^x and g(x)=kx^2. For a positive k, drawing a rough graph of f(x) and g(x) does show 2 solutions of ... 3answers 81 views ### Why Can't I graph (-1)^x? I tried to graph (-1)^x but got nothing. Then I went on and tried (-1)^{3.2} and got -1 as the answer, but when I tried x=3.3 instead I got an error. I know that when x is a natural number that ... 0answers 10 views ### Graph and Stitch Piecewise Function I am trying to develop a model to describe the rate of something increasing. It increases 88983 for 1.26s, then stops for 2.3s. It repeats this cycle indefinitely. The best I could come up with is: ... 0answers 7 views ### Let G be bipartite on n vertices Let G be bipartite on n vertices .Prove that \alpha=\frac{n}{2} if and only if G has perfect matching.. Suppose X\subseteq A and |X|\gt n/2 Then every vertex in B must be adjacent to a vertex ... 0answers 20 views ### Geometric interpretation of the nth root of a quaternion? For ordinary imaginary numbers, (r,\theta) turns into (\sqrt{r}, \theta /2) for the square root and it is similar for higher roots. Is there an analogous interpretation for roots of a quaternion? 0answers 15 views ### How to change position of the axes values of a Sage plot. I am plotting 2D functions on Sage, and I would like to move the values displayed along the y axis (the ticks) from the left of the axis to the rigth, because they bother me there. I had a look and ... 1answer 14 views ### Drawing D=\{(x,y)| |x-1|+|y-1|\leq \frac{1}{2}\} in \mathbb R^2$$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$$. I think I can do this, just need ... 0answers 8 views ### Plot a graph with two inputs and two result I want to plot a graph with two inputs, transmission rate and scan perido, and the result will also be two results, time of detection and number of detected packets. Shall I use two graphs to plot ... 2answers 32 views ### Based on the function graph, in how many points the derivative equals 2? I need to answer the question in the title for this function graph. [] I see that the derivative is positive in 3 segments of the graph, and thinking about it as roughly \frac{\bigtriangleup y} ... 0answers 18 views ### Suggestions for plotting data and representing it on a table I've never been good with graphs so reading up some graphing tips didn't really give me the answers I was looking for. I'm planning to plot some data into a line / scatter graph and unsure how to ... 3answers 23 views ### Sketching the graph of trigonometric functions involving absolute value function How do I sketch the graph of \tan |x|? I know that the modulus over |x| can be thought of as the angle (in radians) will always be positive which implies that the angle is always measured anti-... 1answer 42 views ### Ratios within sine graph Line AB goes from the origin (0,0) to the maximum point of the sine graph at (90,1). Line CD is perpendicular to line AB and is at the point at which the distance along this line between line ... 1answer 23 views ### Defining composite of piecewise function Let$$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\... 3answers 35 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:$-8 = k(x + 1)(x-2)k = 4y = 4(x+1)(x-2)$but the root ... 1answer 22 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 ... 1answer 23 views ### Showing complex transformations in a fluid way It says it all in the title: I need to show how simple complex transformations (translations and dilations, or even both) affect shapes on the complex plane in a "fluid" way – that is, creating some ... 1answer 36 views ### The following graph makes no sense I have been asked to sketch the graph, from x = −5 to x = 5 of the odd function,$f(x)$, defined in the interval 0 < x < 5 by the formula $$f(x) ≡ \cos( πx/ 10)$$ The results I get are as ... 2answers 33 views ### Smallest distance between parabola and line Probably a noobish question, but I've got this problem: Two graphs:$y=0.5x^2$and$y=-2+x$. A vertical lines goes through these graphs in points A and B. What's the shortest possible distance ... 1answer 26 views ### A question about the real line and the Dirichlet function. Though the graph of the Dirichlet function is non-drawable, I think if we have to draw it in some informal way then it will be two complete lines (instead of isolated points). Here's my reasoning: ... 2answers 34 views ### Parametric version of a simple equation I have a simple relation that I need to plot in a plane. I could do it, but I believe that I don't get the best way. A plane curve is defined implicitely by the following equation : \... 0answers 21 views ### Modeling simple linear equations This should be pretty simple but I'm blanking on this. I need to model (graph) how path 1 becomes equally as efficient as path 2 as the distance of path 2 increases. distance of path 1 (from A to B) =... 2answers 74 views ### What would the equation to this graph look like? I have an equation built from obscure (step) functions, which I'd like to approximate in standard mathematical functions; it is quite lengthy and produces an odd geometric shape, which I cannot ... 5answers 63 views ### Solving equations. How would you solve these equations and show that they do not intersect each other? $$x^2+y^2=2x-2y$$ $$x^2+y^2=4(x^2+y^2)^{1/2} +y$$ It's isolating a term which I am struggling with. General ... 1answer 34 views ### Length of wire needed to graph a function Question: $$S = {(x,y): \left|||x|-2|-1\right| + \left|||y|-2|-1\right| = 1}$$ If S is made out of wire, find the length of the wire required. I have no clue as to where to begin this question.... 0answers 43 views ### Graph of a higher-order function When we deal with functions which work on numbers, we can graph them easily: Just take each of its possible input values and find its corresponding point on one axis, then go straight up in its column,... 2answers 67 views ### How to plot this graph$y^3=x^2$I was solving a problem related to area under the integral. When I got a question with the curve$y^3=x^2$. Now this might seem trivial with plotting calculator and for some without plotting ... 4answers 30 views ### Check if a given coordinate lies in path of a ray (coordinate geometry) As shown in the image I have two known coordinate pair A and B and few other known coordinate pairs (RED blob) on the graph. I need to know if any of the other given coordinates fall in line of the ... 1answer 11 views ### How would you plot this equation (in the complex plane)? So I am currently looking at how to calculate the integral of a complex function$f(z)$within a contour$\gamma$. That is, an integral of the form $$\int_{\gamma} f(z) \; dz$$ Where the contour is ... 0answers 31 views ### Finding best fit curve via 2nd order polynomial I've set of data points and I need to best fit curve by using$y = a + bx + cx^2$. I know the method of finding$a,b$and$c$. After getting$a,b,c$; How to use that equation to determine the points ... 0answers 26 views ### Graphing/visualizing a complex parametric plot without using mathematica I am trying to visualize the parametric plot in$\mathbb{C}$of the curve$\gamma$defined for$t\in[-\infty,\infty]$as $$\gamma(t)=\exp\left(-t^{2}+\frac{t}{\sqrt{1+t^2}}i\right).$$ I think I find ... 3answers 529 views ### Absolute value graph sketching Where would you start if you were told to plot: $$||x-1|-1|$$ I looked at just$f(x) = |x-1|$and noticed that the two equations are:$\pm (x-1)$for$x \geq 1$and$x < 1$. Extrapolating then:$\...
These different equations are given in Polar and my goal is to plot them in Cartesian coordinate system: $r = \cos(4φ)$ $φ = \dfrac r {r-1}$, $r > 1$ I am aware of: $x = r \cos( φ )$ \$y = r \...