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

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How to calculate an angled increment on a graph

I'm trying to figure out how to calculate the values needed to make an angle. Like if I have a object at {1,1} and it needs to travel at a 45° to get to {5,5} I would have it increment up the spaces ...
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Graphing the derivative from a graphed function

For the graphs of $f(x)$ make a sketch of the graph $f'(x)$ Here are the sketches I have so far. The graphs on the top row are the original functions. Did I graph these correctly?
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2answers
93 views

Formula to best fit a rectangle inside another by scaling

I am very week in Math. I am a web programmer, and usually my work does not involve too much math - its more of putting records into database, pulling out reports, making those fancy web pages etc ...
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4answers
58 views

Basic question about $y=mx$

The graph of equation $y=mx$ is a straight line... a) Parallel to the $x$-axis b) Parallel to the $y$-axis c) Passing through the origin d) That coincides with the $x$-axis This was a question in ...
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2answers
86 views

How to plot $\frac{2x-4}{1+x^2}$

Can someone suggest me how to plot this function (without any software)? $$\frac{2x-4}{1+x^2}$$ I have found out such points as: $(0,-4)$ and $(2,0)$ I know that $y = 0$ is horizontal asymptote ...
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2answers
31 views

Understanding the translation of a graph (horizontally)

I have been having trouble understanding the translation of a graph. I understand the 'rule in the sense that the '$+$' shifts to the left and the '$-$' to the right when dealing with something like ...
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34 views

Use a table of values to graph each function.

The function is : $y=-x^2+7$ Please help! This is Algebra 1, and we are going over graphing quadratic functions. My teacher is unavailable, so if anyone can explain how to solve these types of ...
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23 views

Transformation/operation to collapse a series of similar lines into a set of constants?

I have a dataset that can be represented in a matrix form as: $$ Y = \begin{bmatrix} y_{11} & y_{12} & y_{13} & \cdots & y_{1j} \\ y_{21} & y_{22} & y_{23} & \cdots & ...
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2answers
45 views

Constructing a parabola from two coordinate values and a peak height.

I am trying to create a parabola function that mimics projectile trajectory. It will input the following: 2 xy coordinates (the starting projectile position and the landing projectile position) ...
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1answer
18 views

find the points on curve that are almost equal

How do I find the points pointed by the arrow in the graph. I.e. the points where the slope of curve is almost $0$.
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4answers
94 views

Best program for 3D plotting

I've hit a roadblock with pgfplots where it has difficulty plotting multiple functions at the same time in 3D. As it states in the manual on page 114, "it cannot combine different \addplot commands, ...
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1answer
21 views

Find a function from graph

I have a greater "trouble". I wanna learn more about "graphs". On this webpage I found some nice graphs in heart shape. And they where written as functions. Another graph I found was "the batman ...
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2answers
57 views

What power of $3$ is $4$?

I am trying to find the point where $y=5$ intersects the curve $$y=1+3^x$$ My working so far: $$5=1+3^x$$ $$4=3^x$$ How do I work out this last step accurately?
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1answer
24 views

Strange log scale on a plot. How do I read this?

Doing an assignment with a strange log-log data plot. You'll notice that there at 14 segments per cycle, and they are not spaced as usual. Note the last 4 segments break the pattern of reduced ...
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1answer
33 views

What are the lines of a surface plot called?

I am wondering what are the names of the specific names of the lines used when a program such as Matlab or Mathematica plots a surface in 3D. They are lines which are the intersection between planes ...
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3answers
65 views

Different Types of Waves

I am making a basic 2D rigid body simulator as a hobby. It involves springs. Naturally, I need to render them. Rigid body simulators, such as Algodoo, render them simply like this Another (more ...
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1answer
14 views

Study of the function $\log(1+\sin(x)+\lvert\sin(x)\rvert)$

I have to study this function. To remove the modulus I split the original function in \begin{cases} \log(1+\sin(x)+\sin(x)), & \text{if $0<x<\pi$} \\ \log(1+\sin(x)-\sin(x)), & ...
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1answer
46 views

Solving an inequality graphically

$$\frac{2x - 5}6 < \frac{x^2 - 1}4 - \frac{x(x+1)}3$$ Should I solve it by turning it firstly into an equation of the form $ax^2+bx+c>0$ and then draw the graph or draw the graph of ...
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2answers
67 views

Please guide me to draw this : graph of $x \geq 5$ and $y \geq 5$

how can I draw the graph for this the graph of $x \geq 5$ and $y \geq5$ is? please guide me to draw it thanks in advance
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2answers
46 views

Average rate of change of $\ln(x)$, decimal slope?

First of all, I'm new to calculus, so please excuse me if my question sounds silly. I have a graph of the function $f(x)= \ln(x)$, and I want to compute the average rate of change of f on the ...
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1answer
653 views

Moriarty's calculator: some bizarre and deceptive graphical anomalies

Background: This is a problem I first came across a few years ago in a calculus textbook (a James Stewart one), where it addressed some of the pitfalls of using graphing calculators. The original ...
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3answers
37 views

how come for any given f(x) a y could have multiple values of x, while x has only a single y value [duplicate]

I guess i might be answering my own question here, but is it because of how we chose to represent our functions? That is, for the lack of better term, strech it along the x axis? Has it it been f(y) ...
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2answers
362 views

Sketch a graph that satisfies the following conditions

Sketch the graph of an example of a function f(x) that satisfies all of the following conditions: Here is what I have so far: Am I on the right track? I think the graph satisfies all of the ...
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1answer
31 views

An ant is walking up a hill. at what x does he see the blade of grass.

've been working on this problem with Mathematica and by hand-help with either would be fantastic. The blade of grass is given by the line segment from (32,1/5) and (32,8). The 2D hill is given by ...
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How can I obtain the the admissible values of each dimension with respect to set of constraints?

when having a set of constants including linear and nonlinear equality and inequality. How can I obtain the the admissible values of each dimension (so-called solution space) . For example, assume ...
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1answer
56 views

Visualizing a volume with MATLAB

I have a rational function $\phi: [0,1]^3 \to \mathbb R^3$ (A NURBS, to be precise) and I want to visualize the image of $\partial [0,1]^3$ using a surface plot (...
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Polar-Cartesian Plot Interconversion

The Question How can we interconvert any general graph of polar or cartesian function so they give the same plot in the other coordinate system. Note: I do not mean to ask about interconverting a ...
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1answer
14 views

With a given point, find the curve that intersects zero.

Background For a pseudo-trajectory of a cannon, I am to find, with a given point maximum $(M_x,M_y)$, the equation of the curve that intersects the origin and the point $(2M_x,0)$. I have the ...
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1answer
52 views

Plot of $\int^x_0 e^{-t^2} dt$

I know that the function is strictly monotone, since $f'(x)$ is always positive, and it is convex in $]-\infty, 0]$ and concave in $]0, +\infty[$ because if its second derivative. However, I am also ...
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1answer
66 views

Prove or disprove that $\sin\lfloor x\rfloor$ is periodic.

The title says it all. I was plotting random functions on my phone and noticed this graph. I don't think this function is periodic (WA also agrees). Is there a way to prove if a function like this is ...
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3answers
42 views

How To Find The Length Of An Irregular Arc

How would you find out the length of an irregular arc. e.g. An arc with a base length of $10$cm and a height of $5$cm - what would be the length of that arc? Is there a specific formula I could use?
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1answer
26 views

How to find equation for a line on a graph

I'm working on something that says the following: Source: http://www.inf.unibz.it/~zini/ML/slides/ml_2012_lab_05_solutions.pdf (solution 2) I can't wrap my head around how they get that equation ...
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2answers
26 views

How to prove that given log function is convex

How to prove that $log(1+e^{-x})$ is a convex function? [from comment]: I have tried with the basic definition of convex function..... like $f(ax+by) \leq af(x)+bf(y)$... but was not able to solve ...
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1answer
42 views

Is there a graphic visualisation of $f^{\frac{1}{2}}$?

$f^{-1}$ can be visualized by flipping the graph of $f$ around the line $y=x$. Is there a similar way to describe graphs of functions to a fractional power, like that one of $f^{\frac{1}{2}}$?
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1answer
30 views

Can someone draw this line $3x(x+1)(x^2+x+2)=16x(x+1)(2x+1)$?

Also the solutions for x are apparently (according to another question I have posted) $x=0$, $x=-1$, $x=-\frac{1}{3}$, $x=10$ But when graphing the line my self the solution are only $x=0$ and ...
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2answers
62 views

sketching derivative of a graph

I am wondering whether or not this is the right sketch of the derivative in the picture below: UPDATE: Here is the function as it appears in the question (please disregard the pencil marks):
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34 views

Why is the graph of 4 nodes and 2 edges not self-complementary?

I am having some trouble seeing why a graph of 4 nodes and 2 edges is not self-complementary such that G is isomorphic to G bar (G complement) (please see the attachment below). I know that the number ...
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1answer
38 views

How (the graphic of) a $\mathcal C^1$ but not $\mathcal C^2$ function looks like

We know examples of functions (obviously we are in the context of real valued functions) which are continous but not derivable; the simplest is $x\mapsto|x|$. In particular we have a precise graphic ...
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1answer
29 views

Sketch $ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $

Sketch the following $$ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $$ I have considered this geometrically and ended up thinking that the complex numbers $z$ must satisfy $$0 < ...
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2answers
24 views

plotting of level curves using pen and paper

I want to plot the level curve for the function $f(x,y)=\frac{y^2-x^4}{y^2+x^4}$ . I tried by substituting $f(x,y)=k$. But I am Unable to draw it using paper and pen. Kindly help me.
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Displaying a 3D function without a graph

I have a 3D function $z=\dfrac{x}{y}$, and I have no access to a function grapher, but I still need to display this function in a comprehensible way. I thought of a table, but even with a domain of ...
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1answer
114 views

Find equation of ellipse given two tangent lines at given points and a point on ellipse

I'm attempting to generate an ellipse for a stair simulation game of mine, and the inputs are: A point on the ellipse The slope of the tangent line to the ellipse at that point Another point ...
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40 views

How to read $y = ax^0 + bx^1 + cx^2 + dx^3 + ex^4 + fx^5$

I'm trying to understand how a performance curve control calculates a graph. The manual says "$y = ax^0 + bx^1 + cx^2 + dx^3 + ex^4 + fx^5$" I get that $y$ is the vertical axis, a to f are the ...
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1answer
56 views

Integration of a function defined by its graph, the union of semi-circles and a line segment

I don't understand how to do this problem and I would someone to help me with it.Please step by step for me. I just started on integration so this problem is a bit too hard for me due to my lack of ...
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3answers
78 views

Easy: Graphs of Straight Line

I can't exactly figure out how to work this out. Well I know the equation for a straight line is $y = mx + c$ $c = gradient$ Therefore if I multiply $3$ by the number $x$ to get the gradient $6$ ...
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1answer
27 views

how to calculate this logarithmic function?

Im having trouble in graphing this log function: $y=\log _{1/4}\left|x^2-5x+6\right|$ I found the intervals: $(-\infty, 2)$, $(2,3)$, $(3,\infty)$ Should I just give $x$ values and find $y$ to graph ...
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52 views

Slope of the secant line given a point

The point $P(1,0)$ lies on the curve $y= \sin(10\pi/x)$. (a) If $Q$ is the point $(x, \sin(10\pi/x))$, find the slope of the secant line $PQ$ (correct to four decimal places) for $x=2, 1.5, 1.4, 1.3, ...
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54 views

Get a function (equation) from data points?

Is there a way to get a function (equation) from data points? For example, we have this famous Google's 'Batman' function: ...
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1answer
48 views

Graphing algorithm

I am not sure if this belongs on Mathematics Stack Exchange, but it is somewhat relavant here. The Problem If you've installed any graphing/plotting apps on your smartphone, you will notice that the ...
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Why $(h,k)$ in equation $y= a(x-h)^2 +k$ is the vertex of a parabola?

As in the title , I know how to convert normal explicit equation to a vertex form equation by completing the square . But what is the reasoning behind why $(h,k)$ must be the vertex , but not other ...