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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2
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1answer
32 views

I've found a MATLAB plot in a book and want to know which command the authors used for the plot

I'm reading a book where the authors write that is a MATLAB plot of the approximation obtained by the method of lines for the finite difference approximation of the Nagumo equation $$\frac{\partial ...
0
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1answer
37 views

Is $f(x) = x^2$ a scalar function?

Take a simple parabola. It is a function that has a one-dimensional co-domain $$f(x) = x^2 $$ It is mapping the set of values in its domain, to one-dimensional values in its co-domain, and it ...
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1answer
28 views

Graph with both slant and horizontal asymptotes

Is there such a graph? A graph that increases at a decreasing rate with the graph approaching a slant asymptote as x decreases to negative infinity while the graph approaching a horizontal asymptote ...
3
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3answers
32 views

Repeated roots of a polynomial

Whenever a part of the graph of a polynomial is in the form of a parabola whose vertex touches the x axis we conclude that a root is repeated at that point. Why is a root said to be repeated at that ...
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0answers
18 views

Plotting y=x^(1/y)

So I was toying around with the idea of recursive functions, where there are two variables, and one of them is on both sides of the equation. I stumbled upon/came up with this function: y = x^(1/y), ...
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2answers
64 views

Solve $11 = 7(2^x)$ for $x$

The Question is ... By drawing a suitable straight line on the same axes , solve the equation $11 = 7(2^x)$ How do I make this equation fit into the equation the graph of $y = 11/2^x + 5 $ ? (...
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1answer
27 views

Sketching $3d-$graphs & parametrization.

I got this question Which I have no idea how to solve or even how to think when sketching, this is the question: Let $f(x,y)=x^2+4xy+y^2$ for all $(x,y) \in \mathbb R^2$. To study $f$ it can be ...
2
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1answer
72 views

Graph of the function $\frac{(x-1)(x-4)}{(x-2)(x-3)}$

We are given the function $$\frac{(x-1)(x-4)}{(x-2)(x-3)}$$ and we have to draw graph of this. We know its domain will be all real numbers except $x=2$ and $x=3$; also, it has a local minimum at $...
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3answers
17 views

How do I plot a linear, exponential and logarithmic function with same starting points?

It should be very basic, but i can't come up with three functions that produce a plot like in the attached picture. I just need some simple format, to illustrate that it is unknown whether some ...
0
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2answers
33 views

Order of exponents matters?

I always thought that $(a^b)^c=a^{bc}$... I am confused about why the order of exponents seems to matter in this particular case: $((x-0.5)^2)^{1/3}$ is not the same as $(x-0.5)^{2/3}$ ...
0
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1answer
28 views

How to plot the differential equation in spherical coordinates with maple

I want to plot the position of Spherical pendulum. there are differential equation for spherical pendulum in Spherical Coordinates. ...
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3answers
40 views

Why does the width of the graph of a parabola depend only on $a$, not $b$?

Lets assume a quadratic function $y = ax^2 + bx +c$. My book says how wide or narrow the graph is depends on the size of $|a|$ My question is why doesn't it depend on $b$ also? If you, say, increase ...
2
votes
1answer
41 views

How to graph $|y|=f(x)$?

This is the image of $|y|=F(x)$ , here the dotted part was the part of the original F(x) is the part that was cut off. $$ y = \begin{cases} F(x), & \text{if $F(x) \ge 0$} \\ -F(x), & \text{...
2
votes
1answer
41 views

What is meant by the “contour of a function?”

Suppose that we have $f(x,y)=(x+y)^2.$ What is meant by the "contour of a function," and what is an analytic expression for it? All software, such as Matlab, Mathematica,.. gives just a function like ...
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1answer
53 views

How can I apply Rolle's theorem here?

How can I use Rolle's theorem to check whether the function $f(x)=x^7+x−7$ has two real roots ?
14
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1answer
249 views

Twin Primes (continued research)

This has become increasingly crowded, so at the onset, let me state this: My question is, is there some reason this is so linear that I'm not seeing? The only thing it seems to indicate to me is that ...
0
votes
1answer
19 views

Differing graphs for simple inverse exponential problem

In class, we are learning exponential functions. The following inverse exponential problem is bothering me: $y=x^{-\frac{1}{9}}$. When graphed, I feel that it should look like it does on Desmos: ...
0
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1answer
37 views

What type of function is $x^2+y^2+6x$?

So, the task is to calculate the volume of body formed when the surface bounded by these functions: $y=x^2/3$ and $x^2+y^2+6x$ rotates around $x$ axis. Everything involving the actual calculation ...
0
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1answer
12 views

Sketch positive area of function with two inputs

How do you sketch an area of a function with two inputs? I have no 3D drawing skills what so ever and I'm having trouble sketching this function. $f(x,y) =\left\{ \begin{array}{ll} \cfrac{4x^3}{y^...
0
votes
2answers
21 views

What does the Cartesian equation of a Parametric function tell us?

I've been taught that a Parametric function can be converted into a Cartesian one by eliminating the parameter $t$ but I've never been taught of how it specifically relates to the Parametric. Does it ...
2
votes
1answer
13 views

Parabola directrix formula

Question 1: I don't understand why (p+x)^2 = (MP)^2 Does it include positive and negative values? Question 2: Why is x + p = 0 Any help is much appreciated. Thank you.
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3answers
43 views

graphing trigonometric functions

I am so confused on how to graph $$y=\tan^3x-\tan^2x+3\tan{x}-3$$ I already have the graph from wolphram however I don't know how to arrive to such graph. I believe I have to write it as a function $y=...
0
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3answers
26 views

Value of k, for an intersection of two parabolas

If $f(x)=x^2 -6x+14$ and $g(x)=-x^2 -20x -k$, determine the value of $k$ so that there is exactly one point of intersection between the two parabolas. How do I do this? If I did $x^2 -6x+14=-x^2 -...
2
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0answers
16 views

Plot complex inequalities $|z^2| > Im(z)^2$

I need to draw the set of all complex numbers, which satisfy the following inequality: $|z^2| > Im(z)^2$ This is what I've already done: $|z^2| > Im(z)^2$ $|z|^2 > Im(z)^2$ - use $z = a +...
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0answers
17 views

finding the equation of a graph with 2 given characteristics

I need to find the equation for the graph of $y = x^2$ with the following characteristics 1. congruent to $4x^2 + 8$ 2. shares the same translations as $\frac{1}{3x - 9}$ I have attempted this ...
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2answers
90 views

Find the highest point on curve defined by intersection of the graph of $g(x,y) = \sqrt{xy}$ and plane $x+y-1=0$

So far this is what I have done: $$F(x,y) = \sqrt{xy} + λ(x+y-1) =0$$ $$F_x = \frac12(xy)^\left(\frac{-1}{2}\right).y + λ=0$$ $$F_y = \frac12(xy)^\left(\frac{-1}{2}\right).x + λ=0$$ $$Fλ = x+y-1=0$...
0
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1answer
18 views

Domain Problems With Equation

I'm trying to graph the equation $y=-2x^{2/3}(x-3)^{1/3}$. I input the equation into WolframAlpha and it is asserting that the domain for the equation is $x \in R : x \geq 3$ and the range is $y \in ...
2
votes
2answers
56 views

Graphical representation of double integral

Consider the following double integral $$\int_0^1 \int_{2y}^2 \cos(x^2) dx\ dy$$ I would have no problem sketching the region if instead of $\cos(x^2)$ I had nothing. However, with the introduction ...
3
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2answers
116 views

Why is the sin of n times pi always 0

My instructor says that $\sin(\pi \cdot n)$ is always equal to $0$. However, when playing with jsconsole.com, I find that this is not the case. ...
5
votes
2answers
58 views

Graph of Composite Sine and Cosine Function

I was playing around with a graphing calculator and I noticed that if you repeatedly apply sines and cosines in this manner: $$\sin(\cos(...{\sin (\cos{(\sin(x)}))))}$$ its graph flattens out. Why ...
1
vote
1answer
36 views

Challenging Linear Programming Question - Determining Objective Function

Working Out: X = Num. of bottles sold from Vineyard 1 Y = Num. of bottle sold from Vineyard 2 A = Num. of bottles demanded by Rest 1 B = Num. of bottles demanded by Rest 2 C = Num of bottles ...
0
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0answers
8 views

Use a uniformed scale to represent multiple linear/exponential equations

I need to allow a user to select a date value ranging from $0$ to $50$ years from a linear slider. There are $8$ uniformed intervals of $(0m, 3m, 9m, 1y, 5y, 10y, 30y, 50y)$. I need a formula to ...
0
votes
2answers
25 views

Incorrect Orientation of Graph in Stewart's Calculus 8E

The problem is #27 (matching graph), and the answer is VIII. I am losing my mind trying to figure out why graph VIII is oriented to have a greater set of Z vertices when X should be the major axis for ...
0
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1answer
72 views

Why can we neglect the negative values when calculating an integral?

Lets say we have the following graphs: Why can we assume $f(x) - g(x)$ for volume and area, even when part of the graph is below the $x$-axis (or will go below the $x$-axis when calculating volume?...
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1answer
32 views

What type of graph is $y=1/(x^2)$

Does this count as a reciprocal graph or am I mistaken? The graph looks like an exponential where x >= 0 although the equation clearly suggests otherwise.
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0answers
25 views

Why is it useful to find the domain and range of a function graph

I know about domain and range but my professor has asked us why it may be useful to find the domain and range and I cant really think of a reason that would be considered "useful". Can anyone think of ...
2
votes
5answers
28 views

Range of a function using graph

If we are given a function $$y = \frac{x-1}{x+2}$$ and we have to find the range . So I tried, I wrote $$y = 1 - \frac3{x+2}$$ $$y-1 = \frac{-3}{x-2}$$ We know this is an equation of rectangular ...
0
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4answers
81 views

Is $x=0$ a local minimum of $f(x)=x^{2/3}(5-x)$?

It seems to be decreasing for values below zero and increasing for values between zero and 2. However $f'(0) = \frac{(-5 (x-2))}{3 x^{1/3}}|_{x=0}$ does not exist. So it's not a local minimum? Btw, ...
2
votes
1answer
12 views

Expressing the Domain of a Function Correctly

Say we have the function $y=\frac{1}{\sqrt{x^2-3}}$ and we are asked to find the domain. So basically the function will be undefined when $x = 0$, and is between $-\sqrt{3}$ and $0$ and also, $0$ ...
0
votes
1answer
11 views

Given a line segment from $A$ to $B$, and a scale of your view of space $sx, sy$, how do you preserve width of line?

So I'm using PyQt5 to do 2D rendering for an LED light show creator app. The light shows are graphs where the $Y$-axis is LED brightness level and the $X$-axis is usually time. I have a zoom feature ...
0
votes
1answer
17 views

Find a constant $b$ so that $\sin(3x)$ and $1 - e^{bx}$ overlap on the interval $(-1,1)$ when graphed

Question Find a constant $b$ so that $\sin(3x)$ and $1 - e^{bx}$ overlap on the interval $(-1,1)$ when graphed. So I know that for the graphs to overlap the derivatives need to be equal. ...
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0answers
14 views

How can I “map” a parameter with range $[0,∞]$ to a “ratio parameter” such as probability?

Newbie in the house! On one hand, I have this sense that there exists one non-arbitrary, a priori or 'natural' function to map $[0,∞]$ into ratio parameter, natural in the sense $e^x$ is natural. On ...
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1answer
32 views

How to graph an implicit function by hand?

Suppose we have a function like $\ln(y+1) - y = x$. What is a strategy for graphing this function without a computer, without a calculator?
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1answer
24 views

Graph a function of two variables online, with the output rendered as color

Are there any online utilities to graph a function of two variables online, with the output rendered as color in some way (for example, red to green, black to white, hue, etc...) Wolfram Alpha comes ...
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3answers
100 views

A way to test whether a function is odd/even using calculator

Could you show me an easy and fast way to test whether a function is odd or even using the calculator ? I've only came across the graphing way and another algebraic way and I'm afraid to make a silly ...
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vote
0answers
20 views

Giving the equation for graphs of fractional powers

In Mathematics Methods we are learning the features of graphs of fractional powers. The equations of these graphs are in the form: $y=a\sqrt{x-b}+c $ By simply analysing a graph with a hyperbola how ...
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0answers
8 views

Graph sketching trigonometric functions

How would I go about graphing sin(sin(x)) and cos(cos(x))? Without use of a calculator I have shown they are never equal to each other. The only way I can go about it is to plug in values and ...
0
votes
1answer
17 views

Plotting a random but continuous line

Hopefully my question makes sense. I would like to generate a function which is continuous at all points. The use of the word "random" is somewhat of a misnomer, since it is not truly random. It must ...
0
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1answer
18 views

Graph $S$ and its image $f(S)$

$$S=\{z: -1<Re(z)<2\}$$ $$w=f(z)=e^z$$ Graph $S$ and $f(S)= \{w\}=\{f(z)\mid z \in S\}$ My attempt: This is what I think it should look like. Correct me if I'm wrong, but I think the general ...