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Question 1

3votes

3answers

187views

Finding a function for $\sin(x)\sec(y) = \sin(y) + \sec(x)$

While messing around on desmos, I discovered the function $$\sin(x)\sec(y)=\sin(y)+\sec(x)$$ which appears as a warped sinusoid glide-reflected to fill the plane (graph in Desmos).Each of these ...

Jayden Szymanski

31

askedNov 25 at 16:53

Question 2

2votes

0answers

61views

Copeland-Erdős constant random walk

WOW! Here are two photos of Copeland-Erdős constant with first 500 digits and first 4000 digits. In Copeland-Erdős constant all prime numbers are presented in order in decimal so $0....

Tuomo Tanskanen

13

askedNov 24 at 9:10

Question 3

13votes

1answer

1kviews

Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?

I wanted to see what kind of properties the numbers just one more or one less than primes would have.I supposed $P_n$ was the $n^{th}$ prime and obtained two numbers from it, $(P_n-1)$ and $(P_n+1)$. ...

Crowbar Jones

149

askedNov 17 at 15:18

Question 4

2votes

2answers

73views

What is the cartesian equation for the graph of the parametric curve $(x,y)= ( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}) $?

The parametric curve$$ \left( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}\right) $$for $t \in (0,1)\cup(1,\infty)$ traces out the points on the graphs of $y = x^t$ which are furthest from the line $y = x$...

Rob

7,626

askedNov 15 at 3:37

Question 5

0votes

0answers

59views

Conditions for the intersection of two weird functions

(From a question at HNUE High School for the Gifted)Let $$f(x) = |a|^{bx}-|b|^{ax}\\g(x) = abx$$Such that $a$ and $b$ are real numbers. What are the conditions needed for $f(x)$ and $g(x)$ to ...

nhals8

11

askedNov 1 at 17:48

Question 6

2votes

1answer

57views

Graphically Self-Referential Function

Does there exist a function $f(x)$ whose graph, when plotted on the Cartesian coordinate plane, visually looks like the expression of the function itself?To explain this more thoroughly, even though ...

Kevin Chen

166

askedOct 25 at 1:32

Question 7

0votes

1answer

73views

What does a 3D plot of a quadratic look like if the z-axis represents imaginary input values?

I recently saw this video about factoring any quadratic expression without guessing and checking.The implication, that I probably should have got sooner, is that $f(x) = 0$ then always have a ...

Tormod

103

askedOct 16 at 7:37

Question 8

0votes

1answer

64views

What am I doing wrong with this Taylor Series expansion

I am trying to find the Taylor Series expansion for sin(x) at $\frac{π}{2}$.I found the series and confirmed it with the key, however when I graph it my solution seems to be shifted down 1 and adding ...

James S.

77

askedOct 15 at 13:27

Question 9

38votes

3answers

1kviews

Given the graph $y=x^4$, can we construct the $y$-axis using only a straightedge and a compass?

This is a question my friend raised and we have had difficulty solving it.Suppose that the graph of the polynomial function $f(x)=x^4$ is drawn on a plane. Can we construct the $y$-axis of this ...

praton

933

askedOct 12 at 15:27

Question 10

0votes

1answer

41views

Is it possible to draw 2d density plot only knowing totals in any cross line

So we see from the density plot that the most dense part happens to be intersection of the x, y histograms where the highest bar meet. But suppose we only have the x, y histograms, I think it's not ...

TurtleTread

203

askedOct 11 at 22:23

Question 11

5votes

1answer

72views

Plotting functions in a way consistent with measure theory

So as far as I understand, modern plotting software work by filling every pixel that intersects the graph of the function. While this works pretty well for contineous functions, it is clear why this ...

Sigma Aljabr

333

askedOct 11 at 2:32

Question 12

0votes

0answers

57views

How to plot the 1-D Wave Equation solution given $u(0,t)=0=u(L,t)$ and $u(x,0)=f(x)$ and $u'(x,0)=g(x)$？

My goal is to create a plot that I can input different initial conditions into and see the effect while sliding the $t$ (time) parameter. But my formulas don't seem to be producing the correct result, ...

Luke Robbins

51

askedSep 24 at 11:17

Question 13

0votes

2answers

97views

How to tell whether a quartic equation has only one turning point?

I want to sketch the equation $y=(x^2+3x+12)(x+1)(3x-1)$, which can be deduced as a quartic with roots $-1$ and $\frac13$ and a $y$-intercept of $-12$.I imagined the equation as having three turning ...

Portly1418

25

askedSep 13 at 10:01

Question 14

0votes

1answer

104views

Logarithmic function, simplification of an expression

The formula for a logarithmic function is as follows:$$f(x) = -3\log(6x+11)-9$$The question is:Suppose b is a number for which both $b$ and $10b + \frac{33}{2}$ are in the domain of $f(x)$ (which ...

pogo-pete

1

askedSep 13 at 5:55

Question 15

-3votes

1answer

108views

Is $f(x)=\max[\{x+1\}, \{5-x\}]$, where $\{x\}$ is fractional part of $x$, periodic or not in $[-2,2]$? [closed]

It obviously seems periodic, I am getting a period of 1, I have made the graph many times, both on paper and on Desmos. I asked Grok and Gemini, both are saying this is a periodic graph, but the ...

scilus

1

askedSep 9 at 20:32

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Stack Exchange Network

Questions tagged [graphing-functions]

Finding a function for $\sin(x)\sec(y) = \sin(y) + \sec(x)$

Copeland-Erdős constant random walk

Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?

What is the cartesian equation for the graph of the parametric curve $(x,y)= ( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}) $?

Conditions for the intersection of two weird functions

Graphically Self-Referential Function

What does a 3D plot of a quadratic look like if the z-axis represents imaginary input values?

What am I doing wrong with this Taylor Series expansion

Given the graph $y=x^4$, can we construct the $y$-axis using only a straightedge and a compass?

Is it possible to draw 2d density plot only knowing totals in any cross line

Plotting functions in a way consistent with measure theory

How to plot the 1-D Wave Equation solution given $u(0,t)=0=u(L,t)$ and $u(x,0)=f(x)$ and $u'(x,0)=g(x)$？

How to tell whether a quartic equation has only one turning point?

Logarithmic function, simplification of an expression

Is $f(x)=\max[\{x+1\}, \{5-x\}]$, where $\{x\}$ is fractional part of $x$, periodic or not in $[-2,2]$? [closed]

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