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
12 views

Can you stretch a function with a zero or undefined gradient?

If $y=f(x)$ is either $y=3$ (zero gradient) or $x=2$ (undefined gradient), is it possible to stretch $y=f(x)$ by graphing $y=af(x)$ or $y=f(ax)$? If it is possible to stretch them, can you only ...
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1answer
37 views

Find inflection points of a function $f(x)=\frac{|x+3|}{\sqrt{x^2+1}}$

For $x\ge -3\Rightarrow f''(x)=\dfrac{3(2x^2-x-1)}{(x^2+1)^{\frac{5}{2}}}$ $2x^2-x-1=0$ for $x=-\frac{1}{2}\ge -3$ and $x=1\ge -3$ For $x< -3\Rightarrow ...
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0answers
46 views

How can I plot the complex function in 2D?

My function: $$sin(wt-jT) \tag{1}$$ where $j$ - complex unit, $T=0.1,\ w=8 \pi,\ t=[0,0.01,0.02..100]$ I transform it to function with real arguments: $$\sin(wt)\cosh(T)+j\cos(wt)\sinh(T) ...
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0answers
13 views

Function representing learning review graph

I've been working on this for a while but am unable to get it right. (If anyone is curious, I'm trying to make a model that determines a user's best time to review something that he has studied, this ...
1
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1answer
40 views

New SAT Math Section: Comparing Equation of Line to Graph

This is a math question on a practice test for the New SAT that will come out in March. These questions should not go above the level of precalc. I'm posting a picture of the problem as well because ...
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5answers
80 views

How to plot the graph of function $f(x) = \sqrt{8\sin^2x+4\cos^2x-8\sin{x}\cos{x}}$?

How to plot the graph of function $$f(x) = \sqrt{8\sin^2x+4\cos^2x-8\sin{x}\cos{x}}$$ Is it even possible ? When I tried it the function compressed into $$f(x) = 2\sqrt{\sin^2x-2\sin{x}\cos{x}+1}$$ ...
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1answer
30 views

Triple Simultaneous Equations not resolving the Equation for a Quadratic Function

so I'm doing this math problem for my Calculus I course in college. Here is a screenshot of the problem: Graph 1 (click here to view); the prompt is "Find an expression for the quadratic function ...
2
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1answer
49 views

What does the double vertical lines in the domain of a function mean?

In my math textbook there was a question to sketch a possible graph in which it gave me some information on it. One of the questions gave me the domain and range of the function. The domain was ...
4
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3answers
64 views

Is this quadratic pointing up or down? How do I know?

The equation is $-2x^2 + 4x + 30 = 0$. I simplified it to $-2(x^2 - 2x - 15)$. To know if it points up, I need to look at $ax^2$, and if $a > 0$ it is up and if $a$ is $< 0$ it is down. ...
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0answers
20 views

From current plot $y=f(x)$ get plot $dx/dy$ vs $y$

I have a plot $y = f(x)$ where $y$ is voltage and $x$ is capacity. Now I want get from this graph the $dx/dy$ vs $y$ plot. How can I get this new graph?
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1answer
31 views

The inequality used to study a trigonometric function's sign has no solutions

The function, sign of which we are asked to study, is: $$f(x) = 2\sin(x)\cos(x) - 1,$$ or, simplified: $$f(x) = \sin(2x)-1,$$ without using its graph to do so, since the exercise itself asks, in ...
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0answers
20 views

How to plot sinusoidal waves of color frequencies?

I'm looking for a function that I can use to plot a sinusoidal wave for various color frequencies. For example, the frequency of red light is 4.6 THz (4.6*10^14 Hz). The frequency of blue light is 6.3 ...
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2answers
44 views

Complex Numbers: How do I know which plane to use?

I'm new to complex numbers and I want to know precisely when I need to use which plane for graphing and a general idea of what the plot would look like. $$z=a+bi$$ When it's in the form above, I ...
2
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1answer
30 views

Plotting the graph of $\operatorname{Re}(z)<2$

$$\operatorname{Re}(z)<2$$ My idea was that, in the complex plane, the graph looks like a ray starting at the origin and extending up to $2$, but not including that point. Then there would have to ...
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0answers
15 views

How can I obtain the equation of a complex signal such as ones obtained from analysing serial buses?

This is an example of a signal I would like to analyse For my mathematics internal assessment, I am trying to apply the Fourier Transform and put a signal through it in order to analyse it and ...
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1answer
30 views

Formula for a bent line

This may be simple, but I don't know the answer. I have the following data: (0,0) (1,12) (2,24) (3,30) (4,36) (5,42) (6,48) (7,54) and so on, the y coordinate increasing by 6 for values above 2 and ...
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1answer
29 views

Complex mapping problem and unsure if mistake in sheet

The following is based on the topic Complex Mapping. Example: Find the image of a straight line $2x + y = 1$ under the mapping $w = (1+i)z + 3i$. Solution: Let us rewrite the mapping ...
0
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1answer
36 views

Calculate curve using 3 points

I'm trying to find a way of creating a curve using 3 points in x,y space so I can use it to find other points. Essentially I have a unit which moves up and down on the y axis and I want to be able to ...
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2answers
73 views

Polar coordinates of an egg-shaped curve

For a simple 3D-rendering project, I need to get the shape of an egg. (actually, a prism with an egg-shaped based). The idea behind it is to explain how a camshaft in an engine is working. From ...
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2answers
34 views

Let $f:[1,\infty)\to R$ be a monotonic and differentiable function and $f(1)=1.$If $N$ is the number of solutions of $f(f(x))=\frac{1}{x^2-2x+2}$.

Let $f:[1,\infty)\to R$ be a monotonic and differentiable function and $f(1)=1.$If $N$ is the number of solutions of $f(f(x))=\frac{1}{x^2-2x+2}$.Find $N.$ ...
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3answers
30 views

How do you plot a graph where $y$ increases in short bursts and not linearly?

I am wondering if it's possible to plot this sort of graph with one equation. Note: the application of what I am doing is for video animation, but I am just asking for the mathematical ...
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2answers
44 views

Once I found the region, How can I found the Area

I have to find the area of the region bounded by $y = 4x^2$, the tangent line at $(3, 36)$ and the $x$-axis. I found the equation of the tangent line, which is: $y = 24x-36$ Both functions meet at ...
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2answers
40 views

What does this mean? (parabola)

The question is: If ($x,y$) represents a point on the graph of $y = 2x + 1$, which of the following could be a portion of the graph of the set of points ($x,y^2$)? The graphs are hard to put on ...
2
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1answer
49 views

Dynamical Systems: Finding Directions Around Equilibria?

I'm struggling to find the best way to determine directions about equilibria in order to draw a phase plot of this non linear dynamical system: $x' = x − xy,$ $y' = \dfrac{4}{5} − x^2 + x − y.$ By ...
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3answers
55 views

How do I graph Linear Programming questions?

So let's say I have the following constraints: $2a + 3b \leq 30$ $a + b \leq 15$ $a \geq 0$ $b \geq 0$ (I just made this problem up, so I'm not sure if it may make any sense when I graph it.) ...
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4answers
102 views

Question about notation, language, and meaning in the context of combinatorics

In my math class today, my teacher defined a function as follows: A string on alphabet $[m]$ of length $n$ is a function: $$ s: [n] \rightarrow [m] $$ To seque back to math from programming, what ...
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0answers
36 views

rotation of spherical surface in spherical coordinates

I need to plot a spherical surface in computer (like the surface of a lens). I know the normal vector (as an example, say $\ n=(1,2,3) $) of this surface and it originates from the centre of the ...
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2answers
50 views

Draw the graph of $\sin(\pi/​2-​2x)$

I tried to draw the graph of this function $\sin\left(​\frac{\pi}{2}​ - ​2​x\right).$ If I understand correctly, this means that we have to shrink the graph by $2$, shift the curve by $\frac{\pi}{2}$ ...
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1answer
33 views

Is breaks in the continuity of a graph scalar with regards to multiplying a constant?

I think I'm probably right but seeing how I've recently begun to go down the rabbit hole in mathematics that tends to produce all sorts of inconsistenties with any advanced conjectures that I make, I ...
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3answers
38 views

What is the function of provided dataset?

x | y 0 | 0 1 | 1 2 | 1 3 | 2 4 | 2 5 | 2 6 | 3 7 | 3 8 | 3 9 | 3 10 | 4 11 | 4 12 | 4 13 | 4 14 | 4 15 | 5 16 | 5 17 | 5 18 | 5 19 | 5 20 | 5 Desmos ...
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0answers
12 views

Inserting “holes” on a graph.

I am trying to plot the set $A = \big\{(x,y) \in \mathbb{R}^{2} \mid x^{2} + y^{2} < 2 \big\} - \big\{(0,\frac{1}{n}) \mid n=1,2,3 \dots \big\}$. I have tried different combinations of set ...
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0answers
18 views

Function for this 3D curve

thanks for your attention. I am trying to plot a 3D surface like the picture below to help depict the relationship between some variables. I have been fiddling with Google Search builtin plotter, ...
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1answer
56 views

How to analytically derive the geometric properties of a hyperbola and programatically use them to graph?

I have the following equation: $$ \left(10^{\left\lfloor\frac{\ln\sqrt k}{\ln10}\right\rfloor-1}+x\right) \left(10^{\left\lfloor\frac{\ln\sqrt k}{\ln10}\right\rfloor-1}+y\right) = k $$ Entering the ...
4
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1answer
58 views

Cis Graphs (Finding Values)

For this question: If you guys are not familiar with the $\operatorname{cis}$ notation $$ \operatorname{cis}(x) = (\cos(x) + i\sin(x)) $$ I've tried doing this: By comparing arguments $$ ...
0
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1answer
26 views

How would be the slope of $f(x)=y=ax$ where $x = \frac{a}{b}$?

Well, in physics we got $W = V\cdot I\cdot t \stackrel{R=^V/_I}{\Longrightarrow} \begin{cases} W = I^2\cdot R \cdot t \\ W = V^2\cdot \frac{1}{R}\cdot t \end{cases}$ In the first case the slope of ...
0
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1answer
48 views

X and Y intercepts

I have a function: $$y =\begin{cases} 3x, &\text{if } x ≠ 0; \\ 4, & \text{if } x = 0. \end{cases}$$ As I understand, function doesn't exist at (0;0). So, what ...
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1answer
45 views

Graphing of $y = (x^2 - a)^2$

I was graphing the equation $y = x^2 - a$ and I know why the graph is a parabola intersecting at the points $(-1,0)$ and $(1,0)$. However, when I graph $y = (x^2 - a)^2$, the graph oddly changes, as ...
1
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1answer
57 views

Combining two exponential distributions onto one graph

In a probability question I am working through, the question says the length of time of a football game, $s$ , is exponentially distributed with a mean of $\bar s$ . It then says to write out the ...
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2answers
51 views

piece wise function question

Let $$f(x) = \begin{cases} 0 & \text{if } x<0,\\ x & \text{if } 0\leq x \leq\\ 2-x & \text{if } 1< x \leq 2\\ 0 & \text{if } x>2 \end{cases}$$ and $$g(x) = \int_0^x ...
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1answer
31 views

equation from exponential graph

I am struggling to get an equation from the graph above I know ${f(x) = ba^x + c}$ When y = 0, x = -2 ${b = -2}$ ${24 = -2a^3}$ ${2a^3 = -24}$ ${a = {\sqrt[3]{{-24}\over 2}}}$
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1answer
28 views

Finding the equation of the line through X number of points?

I have a line graph with $8,000,000$ points. The X axis goes from $0$ to $7,999,999$ in increments of $1$ and the Y axis is either a $0$ or a $1$. There are no fractions on either axis. Is there an ...
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0answers
15 views

plot golden spiral along with rectangles showing the area split

I can see it's relatively simple to plot the golden spiral using the equation: $$r=e^{b\theta}$$ where $b={{ln(\varphi})\over{\pi\over2}}={{2ln({1+\sqrt5\over2}})\over{\pi}}=0.30634896253$ Here's ...
0
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2answers
29 views

Graph of a Function

Given $$ f(x) = \frac{1}{x – 2} + 5 \qquad x\neq 2 $$ Explain how the graph of $f$ can be obtained from the graph of $\frac1x$ by using appropriate translations. Include the image set of the ...
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0answers
71 views

How to Trace a Real-Life Flower Using Polar Equations?

Here is the flower I'm trying to trace: $\hskip2cm$ How can I trace this flower using polar equations? I currently have the formulas \begin{align} r_{1}&=1.75\sin(10\,\theta + 18) +3\\ ...
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3answers
51 views

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 - ...
3
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2answers
280 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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0answers
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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0answers
54 views

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?
2
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3answers
72 views

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 ...
2
votes
2answers
74 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, ...